An entire villa with pool in Tuscany. An apartment with a kitchen. A flat with the view of Acropolis in Athens (maybe you can get that in a hotel, but you can never be sure lest they rebook you to a different room.)
Suite/extended stay hotels with full kitchens are fairly common here, too.
Not true in the slightest. This place ( https://www.airbnb.com/rooms/48299044 ) was an incredible bargain the last time I was in Scottsdale for a couple of weeks, even at $220/night + fees.
For stays of a couple of days, I'll generally stick with hotels, but for anything longer than a week hotels are pointlessly expensive for what you get.
All in, my stay is $1,900 for 3 night. $633/night. Might not be $1,000 a night, but definitely not as bargain-ish as you make it out to be.
I'd challenge you to find anything like that in a hotel property, at pretty much any price.