How does that work when you have to pay rent to a hotel every night (unless you want to sleep on that park bench you mentioned)?
If you stay in the lowest quality motels then maybe it's cheaper than renting or owning a house, but Hiltons are usually quite pricey unless you live in Turkey etc.?
Step 1 - add up everything you pay in rent, utilities, internet, insurance, gym membership, coffee / breakfast etc. No decent hotel will charge you for any of that.
Step 2 - figure out how many days per month you are travelling anyhow because you are passionate about it --> that percentage of your rent becomes the money you are wasting on a really expensive storage locker
Step 3 - realise it's cheaper to give up the apartment than to pay for an expensive storage locker AND to travel...
Nobody is pretending that you can do a 9-to-5 job in London or New York living in hotels. But if you freelance over the internet or at client premises...