The followup question is how do the fast food restaurants offer burgers on the kids menu?
Ah! "Because they have to."
Q: And why does Disney offer so few burgers for kids?
A: Because they don't have to. They have no competition.
The cost difference between offering a kids' burger and a sloppy joe at Pecos Bill's is nil. The ingredients and portions are virtually identical (a kid-sized bun, 2.5-3 oz of hamburger), both require preparation and packaging for service. In fact, since there are no sloppy joes for adults, the kids' meals require an entirely different prep method, the ingredients for the seasoning and sauce, a different method of storing the prepared mix, and different utensils for serving. If they served smaller burgers to the kids, they could simply slap them on the grill next to the adult's burgers.
Kid's burgers
are offered at a couple of other Disney restaurants -- although they are very difficult to find -- so, yes, Disney has figured out a way to serve burgers to children without going bankrupt. I think Lewis has the most plausible explanation:
Disney does not want adults to order cheaper kids' meals for themselves. It's very hard to police and enforce that -- often one parent orders for the whole family, and the other parent is finding a table with the children, so if the family is paying OOP, there is no way for the CM at the counter to know if kids meals are being ordered for children or adults. A kids' burger isn't served at Pecos Bills because adults going there to buy lunch want a burger. They might want a smaller cheaper burger, and be tempted to order off the kids' menu -- but they probably aren't in the mood for sloppy joes or chilled chicken. However, in Morocco at Tangierine, kids can get burgers or pizza. Why? Because adults aren't going to that restaurant with burgers or pizza in mind to purchase for themselves. They want lamb sharwarma, hummus, and couscous.
Disney spends huge volumes of money on seemingly frivolous things like designing garbage bins to go with the theme of an area. The cost difference to provide burgers over some of the less popular choices on every kids' menu at every CS at WDW would be a drop in the bucket to Disney. But evidently, Disney has decided the revenue lost from adults ordering kids' meals for themselves is enough to keep the choices on many of the kid's CS menus boring, unappealing, or not in keeping with the restaurant's theme (ie no burgers at Pecos Bill's, no pizza at Pizzafari). Even so, there are ways to get past the less appetizing choices and feed your kids decently, even well, at WDW -- but you have to be willing to learn the menus, and maybe the adults in the party may need to make compromises on their own restaurant choices.
Until your kids are 10 year old "adults" and order from the same menus you do.