I think this is a fascinating topic. I have a home base, but I just sold it. I debated this for a long time. Should I keep the home base apartment and rent it out? It is in a highly desirable area that makes it easy to rent for the day or for the year. But then if it is rented out I can't just come back and stay there on a whim. I'd have to plan ahead, months in advance and evict the tenant, and then find a new one... ugh is that worth it? Or I'd only be able to come back and stay if a tenant happened to move out. What if that didn't work with my plans?
Anyway, long story short I tried renting it out while traveling for a year and I found it way too stressful. If you have a wonderful manager who can take care of any issues I think it would be the only way I would do it. I think it is a personality thing. I just worried all the time that something would go wrong... and things did go wrong and it was a pain to deal with it from abroad.
Another idea which appeals to me more is to buy something so cheap that I wouldn't need to rent it out - like maybe a trailer or mobile home or something like that. But I don't think anything is cheap enough to make it a good idea (for me). I'd rather invest that money and use the returns to pay rent.
My new plan is to use a small storage space as a "home base". That way I can keep some stuff in a place that I return to again and again. Then I can rent an apartment and still have a few of my own things... my fluffy pillows and blankets, a bike, extra clothes. It's not ideal, but it could be an option if you have 1 or 2 regions that you travel to every year. My storage is less than $20/month which is a lot less stressful than owning a home. We'll see how it works out going forward!
Curious to hear what other people do!