It's just down to tradeoffs on what you're looking for. You can get a kitchen and a bit more space with an airbnb, but you give up on the hotel amenities of support/cleaning staff, and lounge/gym spaces. Don't get me wrong, I usually value a full kitchen over maid service. But I was able to stay at nobu for a comparable price to a 2 bedroom in Barcelona.
I do agree with your point about renting a room in someones place. But that's now a small fraction of airbnb's business compared to renting a full place.
In my experience, hosts have been about half very cool and friendly and half professional, but minimal. My guess is that the people with extremely negative experiences either didn't look at reviews before booking and/or are the type that trash hotel rooms and have issues with spending 2 minutes cleaning up after themselves. Ask anyone that's worked in hospitality: that type of person is sadly very common.
That being said i had an excellent experience in Switzerland. My host went off Airbnb soon after that and launched her own website.
It's not that everyone else, or you, are necessarily wrong about which is cheaper. I suspect you just plan your trips differently or with a different timeline than other commentors.
I can’t imagine this is limited to Europe, either. I’m not familiar with the new NYC law, but assuming it doesn’t affect bedrooms, only full apartments: it’s absolutely cheaper than a hotel. Good luck finding a hotel for less than $100 a night anywhere in the five boroughs.