I also realized I'm dumb, you can't really mash raw carrots.

I'm still not convinced that putting in a kitchen is a better approach than having parents bring food; parents need to feed their children at home anyway, so they're going to have food. And if children have specific needs, parents will be better able to handle those as well. (For instance, the room my kid is in has children aged 4-10 months - the very small kids can only drink milk, mine is at the age where she can eat some pureed foods, and the older kids are happily eating crackers and other stuff.)

Kitchens also take up space - which is probably a bigger concern here in New York than your rural area.