Isn't that kinda what you're suggesting here? Most piles of trash aren't caused by homeless, its residents, so why should they need to be responsible? Residents could just buy their own cans as its their own problem
The homeless aren't exactly the best workforce. For many, there's a reason they are homeless despite plenty of support systems that helps people become more 'homeful'.
Similar, but generally less so, for some of the unemployed.
If you want to 'mobilize' people, just advertise jobs normally and use a normal hiring process. One that should, of course, be open to currently homeless or unemployed.
Humans struggle in urban environments to resolve problems because “someone else should”.