Those fines pay for enforcement. They also pay for picking up garbage dumped by unknown persons. This model shifts the burden from everyone to just the offenders. I find it preferable to small households subsidising big ones.
[1] http://www1.nyc.gov/assets/dsny/downloads/pdf/about/laws/DSN...
That's what your argument basically boils down to.
Obviously it's not in our collective best interest to have trash accumulate on the streets. So we all end up paying for it collectively, regardless of how much we consume the service as individuals.
Economically, clean streets are non-rivalrous (my clean street costs little more than my neighbor's) and retroactively excludable (through fines). This makes it a public enterprise good, akin to mail or trains [1].
Case in point: mattress and A/C sellers in New York City dispose of your old mattress or A/C for you. If pick-up of such things were free, fewer would do that. One response might be to regulate every thing one might purchase that could produce big trash. The other is to just make people who choose to make big trash pay for it.
[1] http://www.pitt.edu/~upjecon/MCG/MICRO/GOVT/Pubgood.html
I don't produce lots of big trash. Not sure why I--nor anybody else--should subsidise people who produce lots of big trash.