My touring has been on the trans america an similar routes ans I wouldn't even consider leaving my stove home. I eat in diners quite a bit and also eat cold food some of the time, but I also want hot oatmeal in the morning some times or a hot meal in the evening when away from town. On the TA we used a canister stove and when we had trouble finding replacement canisters we really missed having a working stove.
I figure there is very little to gain by leaving the stove home even for a weight weenie like myself. If I take my full kitchen setup it is about 12 ounces. That inclues a Ti bowl and .6 L cup, as well as my Ti spork some other small stuff (lighter, etc). The stove portion is home made pop can alcohol burner plus stand and wind screen that all weighs about 1.4 ounces depending on which pieces i choose. I take most of that stuff whether I cook or not so there is maybe a 2 ounce penalty in hardware fr taking the stove with the alcohol burner. Of course it needs fuel, but I can carry the stove and only buy fuel when/if I decide I want to cook. In my case I always do, but someone who is unsure could have the option, but carrying only the 1.4 ounces. I buy a 12 ounce bottle of yellow bottle Heet and use the bottle it comes with as my fuel bottle so there is at most about 14 ounces of extra weight carried.
My heavier liquid fuel stoves weigh closer to a pound so the weight is more significant. A canister stove with the smallest canister is a pretty light option for the once in a while cooker and you could pick up more or a larger canister if you decide to cook on a regular basis. I might commit to one of these two types where I want to be able to use a stove where there will be fire bans requiring an off switch/valve on the stove. Also both types are more suitable for groups than my pop can stoves which are best for solo or at most two people.
The average TA rider is probably going to be 10-12 weeks on the road and there will be times and places where there will often not be restaurants to eat at. It is a long haul and maintaining some kind of normalcy is helped by being able to at least heat up food IMO. It will pretty nice to be able to heat up food if not actually cook anything elaborate. Camped in the middle of nowhere I enjoy pulling stuff like instant oatmeal or ramen noodles (I add a dash of hot sauce and sometimes some hard cheese) out of the bag and heating them up. It is nice to cook more elaborate meals to, but most of the time when solo I don't bother getting too carried away. Travelling with company we have fixed real meals with a nice bottle of wine and all.