The main issue with the backpacker type acoustic guitars is that they sound WORSE than the new el-cheapo Acoustics that are playable but not rugged and durable.
Even Martin's backpacker sounds poor though it is reasonably well made for what it is. You just cannot get something (acoustic) that sounds decent enough with such a limited size body...........well it isn't so much a limited size body because it really isn't a proper body but more like a cigar box....
As mentioned already by others, the road shock and bumps, not to mention excessive heat will assist in the destruction of an acoustic guitar almost as fast as Peter Townshend was able to destroy a Gibson SG during the end of My Generation finale of their shows during 1967-1969. Pete broke all kinds of electric guitars that would be extremely valuable today. It is reported that he was able to snap in two, the SG, the fastest because its set neck has less "meat" than say other set necks or bolt on like Fenders. Pete didn't discriminate as he broke nearly every model electric, as the Who Concert File book even reports on the exact color and model guitar broken if photos and newspaper reports documented it.
Typically, the only really good acoustic guitars in the sub $600 price range are made by YAMAHA. This is my professional opinion. There are no exceptions as nothing exceeds a YAMAHA at any price point under about $1000. You can obtain a good sounding new YAMAHA for less than $200. You're likely to find that most others in the under $200 price range will not be as predictable. The others might sound okay, and one outta fifteen might sound nearly as good as the Yamaha bare bones entry model. Having said that, the "TRASH" acoustic guitars that are currently coming out of Chinese factories today are better than the affordable American made acoustics of the 1950's and 1960's that intermediate players & beginners developed their skills on at that time. The necks and fretwork are better and the action outta of the box is playable, and machine heads, the intonation and overall sound is better. What is bad is that the fret ends will probably be razor sharp, needing slight sanding, and you'll likely need to remove the saddle and with a sanding block or flat file, will need to remove some material to Lower the action a little bit but pay close attention to the limitations of what is prudent because you want the guitar to be playable across all the frets and you do not want fret buzz. These "TRASH" acoustics don't sound horrible, as they do sound better than any travel guitar but their body construction is somewhat fragile and you'll have the inner braces become unglued or cracked and the bridge might lift or become totally unglued if really banged around in the intense heat of Summertime outdoors and prolonged exposure to direct sunlight. ......................STILL YOU CAN FIND new $60 "DISPOSABLE ACOUSTICS" that will be playable and sound okay...........indoors in even an un-airconditioned home where temps might range from say 59F to 85F, these "DISPOSABLE ACOUSTICS" should last for a minimum of five years, but strapped to a bicycle even with heavy padding could reduce that to as little as Day(s), or a Week if road bumping begins to destroy it.
-----------Go to the bay and search: guitar
You'll see the el-cheapo acoustic offerings from Musicians Friend there, the very junky ROGUE RA-090 for $56.99 and the junkpile Rogue RD-80 for $59.99. There is another similar Rogue model called the RD-100 which is junk too that might be about the same or perhaps more durable but around the same price. All will be playable and will be somewhat lacking in low end but with decent strings and sanding the sharp fret ends and perhaps lowering the saddle by sanding/filing, they aren't horrible if the new guitar arrives to yourdoorstep without a cracked or warped neck, or damaged body.
There are massive ebay sellers with bay names like mulchoice, city-green, millionshare, yallstore ..........that sell a huge number of playable junky acoustics which are sometimes better than the ROGUE cheapies, but don't expect anything better or worse. See 174602156110 , a Glarry branded acoustic for $49.99........there are other models from Glarry, all are junky like the Rogues but playable until they destruct or the bridge lifts off. This assumes you get one that has no issues upon arrival!
The machine heads (tuners) are adequate and are better than one would expect. There also exists a relatively new el-cheepo Ovation-IMITATION at the sub $70 price point see # 133493119848 and 174602159669 . There is also another salad bowl plastic back, see 174621585027.
IF YOU'RE LUCKY, PERHAPS you can locate an old FG-75 YAMAHA acoustic from the seventies.......why this model? the body is a very small parlor like guitar body, yet it sounds nice (not too much volume though..) and a 25" scale which all Yamaha FG series had until about 1994 or so. The FG-75 was made and sold in the early 1970's and I think it was discontinued after the mid seventies. The problem is locating one today. Nobody wants to get rid of these unless age has caused the action to rise such that its unplayable without a neck reset. The FG-75 has basic low quality open tuners but every thing else is on par with the quality of todays $400 instruments. Its very small size body might survive if packed and protected. Yamaha made a superb laminate top guitar and the woods used for the sides back and neck were first rate on this base model back in the seventies. TODAY, you can't find such a small bodied acoustic of the same quality for less than maybe a grand.
The smallest available bodied YAMAHA today is in the FS series, the FS-800 which is the same size approximately as the FG-150 (of 1969-1972), and the FG-170(of 1973-1974)and the FG-331(of late seventies).....in about 1981, this became the SJ-___ series until they later on revived this as FS-___ series. ALL have a 25 inch scale. Those are the smallest bodies of YAMAHA. Other FG series from seventies, eighties, until approximately 1994 have typically the standard yamaha size body and 25 inch scale and laminate tops with a few exceptions. In around 1994 the bodies of the were widened by about 5mm and a longer 25 1/2 scale length was adopted for the FG series. The F series came into being as the low end laminate top with the 25 inch scale length.........somewhat similar in body size to some of the most popular FG guitars of the seventies except that the seventies era and early eighties FG series featured top quality woods at the base models where the F series does not, now or then during the nineties. If you can find a used basic laminate FG or F series for less than $100 and don't mind subjecting it to getting beat up, that should provide your best sounding acoustic, given that should you subject any solid-top acoustic to road travels by bicycle and your solid-top quality guitar will be sounding as bad or worse than a $50 chinese cheapie........worse means it will get broken and become unplayable.......plywood top(laminate) can better survive the rigors of outdoors and road shock/bumps and temperature-humidity changes. ....No reason to expose a great expensive guitar to possible destruction!
There is yet another, possibly practical avenue of guitar travels. There are $56 stratocaster copies that are pretty decent. They are lightweight because the bodies are thinner and slightly smaller. They have pretty good necks which are baseball bat chunky in shape. The fretwork is pretty good and uniform, though you likely will encounter sharp fret ends that need sanding. The necks are completely without any finish.......bare wood like a baseball bat. Some are all maple with maple fretboard and some are maple necks with rosewood fretboard. The body paint/finish is really good, as is the fitment gaps on the bolt on neck joint. These would be phenomenal guitars at 3x the price. $55.98 rosewood fretboard strat copy #371894901022..................all maple neck strat copy #373196990664 also see #373271209025 for $69.99 tele copy and #313189523745 for a semi hollow tele with humbucker in neck position.................unbelievably good for 3x the price, and you can imagine the possibilities if you are a decent guitar player and you know something about set-up and modifications. I could tell you a whole lot more but that should get you started. Don't worry those are the typical selling price throughout the year, price only goes up sometimes during the summer and goes down and up slightly between Sept and early Nov before going on back down for Black Friday thanksgiving season.....you get the picture....
Oh, up until late 2018 the headstock shape mimmicked the fender cutout shape on the strat copies but since then the headstock cut is just as you see there. These are good playing instruments which have decent sounding pickups. Unbelievable, that they are available for $55. You can find LEFT handed versions of both the strat copy with rosewood fretboard for approx $85 -$90 from some of these sellers too......ditto on the LEFT handed tele copy for about $88 but be forewarned that neither the Right handed or Left Handed tele copies had been available until 2020 or late 2019, and there wasn't much supply of those.......it appears the chinese factories are producing more of the t-copies. I hope this helps. As for battery powered amps, VOX made a decent one about a dozen years ago, but it isn't small.....you could get a tiny HONEYTONE which retails for about $25.......It isn't too good but it is tiny and battery powered..............You can also build a punch amp or the smokey cigarette amp but they don't give a decent clean tone......there are plenty of other batttery amps from the 1970's pignose to who knows what....you'll figure it out if you look at all the possibilities...............heck you can practice on the strat copy without an amp.............but you can find or build something useful as a small battery amp.