It really is bad government. The city council should make a tender and have the local utility come and collect big items for free. That's how it works in the European city I come from. And the utility taxes are all but high.
I think the free service was born out of despair for people consistently leaving big trash on the roadside. While I understand you as I don't produce big trash myself, I guess it's still better to just pay a little more and get rid of the bigger problems having trash on the roadside would bring.
New York City fines people $100 to $400 for using improper receptacles, leaving receptacles uncovered, putting trash in front of others' buildings and/or leaving loose rubbish lying about [1]. Note that these can accumulate, e.g. if you put loose trash in front of someone else's building in an improper receptacle, that could be $300 to $1,000 of fines.
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.
How do you demonstrate that the fridge left on the side of a public road, even if close to someone's home, actually belonged to someone? The examples that you mention are even harder to enforce. Cameras?
My house has never had a fire, so why should I pay for a fire department in my neighborhood?
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.
I have less control over whether my house lights on fire than if I make lots of trash. Also, if my house starts burning, it's an immediate threat to my neighbours' safety. If I leave trash outside, it's a less-immediate threat to their comfort.
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.
But I already do have large item pick-up funded by the city or whatever. I basically never use that service and have no idea when it is. My standard operating procedure is to just put this large eyesore out in my front yard and eventually the government will come pick it up. Either that, or often times private citizens will recycle whatever it is for money.
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.
Check with your city, if Waste Management pickups up your garbage you might have three free pickups a year on top of the yearly large item pickup. For the scheduled ones, we usually get a mailer a few weeks before they come up.
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...
Why should they? If there are dangerous items to be disposed that 99.99% of the people on a given garbage day don't throw out, should the other people subsidize the disposal? Most residents are not throwing out things that need special care. By making the price more transparent, you can incentivize people to use fewer items that are toxic or bad for the environment.
The other side of the argument is that people simply won't do it. If you make it difficult to dispose of used motor oil, people will just put it in their regular trash bags and it will wind up in a land fill where it's dangerous.
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.