If you're going on a longer trip, then a regular, full-sized bicycle is preferred. Bike rentals may fit the bill, but not always. Riding your known, tried-and-trusty steed is usually the best way to go. Folding bikes are really intended for the frequent "ride on a bus, hop off" type of usage. Quick mixed-transportation commutes, or bringing on private aviation. Long-distance, loaded touring isn't that well suited to most true folding bikes.
I took a two week France trip in May. The only mechanical issues we had were on the.... you guessed it... RENTAL BIKES! One nice Ultegra carbon road bike had a stripped through axle. The rear wheel would NOT properly tighten. How you strip a through axle eludes me, but someone did. Worse, the rental outfit sent it out like that! For shame! Bicycle Adventure Club has had similar experiences with rental bikes abroad and they prohibit their use as a result.
A Ritchey Breakaway or other bicycle equipped with S&S couplers allow you to fit your regular bicycle into a standard-size suitcase approved for airline travel. No extra size penalties, no extra cost. Just come in below the 25 kg weight limit and you're (almost always) good and won't be charged. Go with a hard case and your bike is indestructible (obviously within limits!).
However, put an AirTag in your bike luggage! (Despite what Lufthansa is trying to pull!) I realized AirTags would be a REALLY good idea for our two tandem suitcases. Sure enough, we arrive at our destination and only ONE suitcase arrived. OH NO!!!! (I think getting HALF a bike is worse than no bike at all!) I check on our AirTag and sure enough our suitcase is at baggage claim at our LAYOVER airport!
Luckily the airline got us our other half just in time for our trip and disaster was avoided.
That said, break down and reassembly of a packed bike with S&S couplers is an ordeal. 2-3 hours, more if you've been indulging in good French wine or German/Belgian beer!!!! So if you're going for a long ride or tour, this works. For frequent travel, it's not ideal.