Well actually, speak of the devil, I moved out of my last apartment specifically because my downstairs neighbors, who had lived there for years, were completely intolerable. If I could have waved a magic wand and replaced them with an AirBnB crash pad, I would have done so in an instant. Restrictions on short-term rentals are of little comfort when your long-term neighbors are worse. Then again, the arguments against short-term rentals go through just about as well for long-term rentals, so why not just restrict rental properties altogether? Many homeowners seek to avoid neighborhoods with high rental density, so why not make their jobs easier with a law?
As I said, there are plenty of attributes that make different houses more or less desirable to different people. If the OP had converted their apartment into a sarin gas factory or a practice pad for MBV, it might be a little more understandable why regulation would be efficient. As it stands, having a short-term rental next door strikes me as an extremely vague sort of source of disutility: all you can say with certainty is that you won't have long-term neighbors. Which many people are fine with in the first place. If people have varying preferences about living next to short-term rentals (either because they view them as a source of variety in se or just don't mind that much either way, as I do) then it should be more efficient to let people figure it out for themselves. People already self-assort into spatially resolved communities according to many other attributes (e.g. school quality, proximity to nightlife, population density; all attributes which reasonable people can value differently) so it seems strange to pick 'proximity to a short-term rental' as the one intangible neighborhood-character issue to treat like 'proximity to a meth lab'.
So let me just state again: I wouldn't mind living next to a short-term rental. In fact, if they're as widely despised as you suggest, I'd mind it even less because the housing market would be effectively subsidizing my tolerance.