If you want to stay at a place that has a kitchen, and multiple bedrooms, there are suite hotels (eg. Homewood suites) and extended stay hotels. If you want someone to host you, then a bed and breakfast is another type of accommodation.
- Not wanting staff or service.
- Wanting something that looks and feels like a home rather than a hotel room. This isn't available everywhere.
- Wanting something that isn't shared with a bunch of other hotel guests. (Aside: I have no problems with apartment buildings banning AirBnB/VRBO, because that's much more "cheap hotel substitute that might bother neighbors" than "unique offering that isn't likely to bother anyone".)
- In general, wanting something unique that doesn't tend to exist as a hotel.
Whatever the case, despite the existence of the options you list, Airbnb's are still popular. There's clearly some significant differentiator between them and an Airbnb.
But there is a psychology to it that is, as you say, hard to pin dow. A hotel that has a random assortment of plates and cutlery in the kitchen (like my last AirBnB did) would feel cheap and tacky. The AirBnB didn't.
2. 3+ bedrooms. Good luck finding that in Hotels.
3. Things like private hot tubs or pools, BBQ in the backyard, etc are almost unheard of in hotels.
4. Laundry machines.