I don't produce lots of big trash. Not sure why I--nor anybody else--should subsidise people who produce lots of big trash.
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
So if this service rolls out in my area, I can either leave this large piece of garbage in my yard for a week or so waiting for the government to come pick it up, or I can open an app on my phone and have someone pick it up today.
Here's the description from a random city:
For items that are too large to fit into the trash cart, residents may request the free pick up of household bulky goods three times per year. We will retrieve up to four large items such as furniture, appliances or up to 20 plastic bags of refuse or bundles of yard waste (less than 50 pounds each) for each request. Advance notice is required. To schedule a free bulky goods pick up, please contact Waste Management...
The towns around where I grew up used to make you pay money to get rid of metal (!!!!). Consequently it wasn't uncommon to find washing machines and old rims in random places. Then a scrap place opened up, appliances stopped showing up on the side of the road and the scrap place that only took copper quickly got ran out of business.
People don't want to dump stuff illegally, it's just the least worst option in the moment.