Then you didn't have a tight fitting lid. Maggots come from fly eggs. To grow maggots, you need a moist place where flies can lay their eggs. Then after a day, they hatch. If you have flies in your home, and they are landing on your diapers and hanging around long enough to lay eggs, this is possible. But I'd be more worried about the flies all over your baby.
A few thoughts about cost -- A diaper service doesn't save you any money, probably. If you are proactive with plastic and buy from Costco and never from Walgreens, you can spend less money than you would with a service. I expect we spent about what an average American spends on diapers.
There are some people who believe that cloth diapered kids get out of diapers more quickly (they are more aware of being wet than plastic diapered kids). If you can cut 3-6 months off of your diapering life, that is a significant cost savings, whether you are using disposible or cloth. We switched to plastic for the last bit of time until my youngest was potty trained - and that dragged on forever. Who knows if it was related, but it was a much more difficult process than with the cloth diapered kids.