Yes, actually, at least for basic pickup. I'd support it for big/dangerous items as well. It is really easy to let that trash bill go if you get poor, and folks tend to dump things when convenient or burn things that shouldn't really be burned to get rid of their trash. They leave large items in rentals they are moving out of and put dangerous items in with the regular trash.
Sure, communal pickup is flawed - but so far, it seems to be the better solution.
The trash bill for the poor is that for weekly pickup. Luckily, many poor folks live in cities, where the cost is included in taxes. Get outside city limits in somewhere like Indiana, and you have to pay.