Silas has already come up with a good response, but...let's say this was implemented. And let's take the standard economic oversimplification of assuming mostly self-interested people.

And let's say I live in an apartment with six other people, one of whom is noisy. Five people are considerate and respectful of their neighbors, one is an inconsiderate asshole. I pay the asshole $100/month to do what everyone else does because they're a decent person. End result: being an inconsiderate asshole earns you $100/month. If you value fairness, this is already a bad outcome.

Now the other five people are upset, so they start making noise in the hope that I pay them $100. All this noise makes everyone unhappy, since everyone has at least some noise intolerance, and I don't have $500/month I can give away. I try to renegotiate the contract with the asshole, and he refuses. The other people can't back down, because they know this would ensure that they would never be respected as a bargaining partner again because even if I didn't pay them the money they would eventually stop making noise. The apartment becomes intolerably loud. This is an extremely bad outcome.

It becomes tempting to suggest that now everyone in the apartment make a deal, in which everyone who wants quiet pays a certain amount to everyone who wants to make noise, with the amount of money depending on how much each person believes in their individual preference. However, if you're quiet, there's a strong temptation to say you're actually loud in the hopes that other quiet people will buy you off. And if you're loud, there's a strong temptation to demand more money than your loudness is actually worth to you: that is, even if you don't really enjoy being loud, you should threaten to be really loud unless the quiet person agrees to pay you the absolute maximum amount ze can.

I read once about some people who tried paying kids for getting good grades (my memory is very hazy, I may be confusing some details of this study). They found that if they paid kids a small amount for good grades, their grades actually went down. When the kids weren't being paid, they were thinking in terms of "Do I have enough intrinsic motivation to want to do well?" and the answer was very often "yes". But when the kids were paid, they were thinking in terms of "is this amount I'm getting paid worth the effort of getting good grades", in which case the answer was very often "no". I think the same thing could happen here, leaving everyone worse off.

And finally, there's just plain ethical ramifications. Imagine an apartment with six people, some of whom are rapists. The rapists want to rape the non-rapists, and the non-rapists don't want to be raped. One solution would be that the non-rapists pay a certain amount of money to the rapists each month to incentivize them not to rape them. The other solution is government regulation. I think the government regulation solution comes a whole lot closer to our intuitive ethical conception of who has what obligations.

[another easy solution: simply have landowners or other nongovernment entities designate certain apartments or neighborhoods as "quiet zones" and others as "party zones". My old college did this with its dormitories, and it worked fine. Unfortunately, I have never seen this implemented in the real world with any sort of rigor.]