Even if you’re a perpetual traveler, you can’t be a tax resident of nowhere. Banks and brokers require you to give them a foreign tax ID and a permanent residence address. See https://www.irs.gov/pub/irs-pdf/fw8ben.pdf
I wonder if Paraguay is a safe option for this purpose? Do you know anyone who’s happily using their Paraguay tax ID and address with banks?
Here’s what I mean by safe. You have an existing US/UK/EU/etc bank account. You contact your institution to update your info on file. If you list an address and tax ID from a country like UKR, RU, Seychelles or Vanuatu, your bank would probably close down your account. Such countries are not safe options.
Also, any ideas on Mexico instead of Paraguay? I see that largest brokers are open to Mexico but corruption and cartel might cause some future problems?