Putting a coke bottle in a recycling vs trash can does nothing to reduce its probability of ending up in the ocean. But doubling the number of trucks picking up waste at my house does double the CO2 emitted into the atmosphere.
There is an entirely separate, less frequent service that collects organic waste, so there’s probably some overhead there.
The line you're drawing to define "labor done on behalf of a paid service provider" is laughably ridiculous. The service they provide is "picking up sorted bins of trash". You're not "doing their work for them" to meet the terms of the paid service agreement.
https://www.aoausa.com/magazine/?p=4982
I bet, each city, that enforces waste sorting, has a monopoly.
This is insanity on stilts.