Sounds like a dream to me, as I live my life on a 3 city rotation like this. Practically speaking, I just rent a house seasonally which is not so hard to do. There’s a small premium, but then I get to keep my equity in the market instead. A lot less headache and someone else gets to worry about the hurricane heading right for my Oct to Jan rental.
This is an area I’m passionate about and am willing to start something if I can see the demand. Setup a form here if you want to reply: https://forms.gle/A6u433hGYSsybeig6
The equity part is a good point. I think the math can work out so that it’s similar to the existing buy vs rent issue people have for a main house.
A nomad style appeals to some people for a (often short) window in their lives. As you say, mixing that up with a bunch of property ownership seems a lot less appealing as a practical matter.
Plus, several times now we have changed one of our bases for a new city. Much easier to call up a short term rental agency and get a new furnished rental.
I've thought of making a portal connecting people like this before, especially digital nomads.
Find a group of DNs who like the same countries as you (think a circuit), pool money to buy property in the 3 or 4 countries, then just hop over.