The recycling is funded by the county landfill. If they stopped accepting recycling from municipalities, they would get more fees at the landfill. They could also put in a tax to fund the recycling, or start charging for recycling drop offs.

Let's go with "small town Midwest".

Normally, the reduction in landfill fees is counted as a saving in favor of recycling, interesting that in your case it's the opposite and seen as an income stream for the people deciding whether to recycle or not. Sounds like a political problem, though I accept that in theory there could be places where it makes neither economic, nor ecological sense to try to recycle. I'd only really trust a proper expert analysis on that though, as it's quite complex (e.g. if you profit from recycling A, but it costs you to recycle B, does it still make sense to recycle both if some of the cost are shared by both materials)

The same entity runs the landfill and the recycling program. It's done to lessen the rate at which waste goes into the landfill, so landfill tipping fees are used to fund the recycling. They don't particularly see the increased fees as an income stream, but they would be a consequence of not accepting recycling anymore. I guess the motivation is that as long as the costs are low, the recycling program reduces capital expenditure on the landfill.