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.
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.
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.
- 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.
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.