There are usually enough pizza places in the main business areas that any place that is crappy will suffer quickly for business and go under. I have run into the odd slice or 2 over 40 years of experience there that was not amazing, but I have found there is good pizza and even better pizza. Even better you need to hunt around a little for, but easy to find with some effort. Garbage days are the only really smelly days, especially when it is really hot out, but there are a lot of cars there and subways and sewer smells at times ...Here's the thing - not ALL pizza in NYC is good. It is quite possible to get crappy pizza in NYC.
The reason NYC is proud of its pizza, and its bagels, is not that they are always good in NYC. It is that good examples are easy to find in NYC. Go to a neighborhood, try just a couple of places, and you will find a pizza you like.
There is competition, yes, but "good" is not the only thing that rises to the top in competition - low price and convenience do too. If a new Yorker has got half an hour for lunch, they go down to the street, walk into wherever is close by and cheap, and will shove a slice of greasy floppy gunk down their gullet and get on with life.
New Yorkers will not whine about crappy pizza. Just like they don't whine about how the streets are often kind of smelly. New Yorkers are insufferable because they have a shared bond over putting up with crap. It builds character. And if youse can't hack it, they don't need ya.
This is actually a nice time to visit, not hot or cold so you can walk around much easier.