I feed carrots (with other veggies) all the time because they don't mold and they are like 45 cents a pound at Walmart. So I over feed the carrots, then whatever else I feed, I try to make sure it is consumed within 24 - 48 hours. And bugs do seem to prefer food they haven't had in a while. Since they have carrot, pretty much 24/7, when I drop anything else in there, the roaches will come off the carrots to get the new food. Roaches that aren't currently eating, will come out of hiding to eat the new food. I seldom have mold or wasted food this way.
I really take an interest in feeders. I'm weird like that. I don't feed prepared food other than some rabbit food for protein. It takes weeks for them to eat a hand full of pellets because they prefer the fresh veggies.