The EU has laws for that and countries with communal bins are doing just fine.
Communal bins are even better for sorting trash as you can easily have seven different types* next to each other. Nobody wants seven personal bins in their yard.
https://eeb.org/en/library/explained-europes-new-laws-for-se...
* paper, textile, plastics, biowaste, chemical/oils, glass, other
Here the rate per kg is different depending on which bin it is, so you're "rewarded" for sorting properly.