Just to be clear, a broker will usually only ask for a utility bill for their KYC. So it's easy to lie. Of course if you go for a fake Dubai residency (which will cost you several thousand dollars every year), you can say you're resident there and probably no one will ever find out.
But WHY would you do that when there are so many countries where you could just live tax-free since you're living off capital gains? Why would you go for some dodgy setup?
Yes, having no tax residency can work in theory because you'd be "falling through the cracks".
But in︀ practice, all banks, all authorities, everyone always assumes that you must have some place where︁ you live.
The concept of perpetual travel is not something that really exists in the︂ law, so there is always some risk that one day, some country will say: "Well,︃ if you don't live anywhere else and you spent more time in our country this︄ year than in any other country... Then you're now tax resident in our country!"
Simply because not all countries have clear rules for tax residency (substantial presence). Many countries just︅ have a rule like "If you spend 183 days in our country or if your︆ center of life is here". Then if you spend 4 months there every year, there︇ is some risk that they say it's your center of life, especially if you don't︈ have an official tax residency elsewhere.
So just take your pick, Portugal, Cyprus, Malta, Georgia,︉ whatever, some country where you want to spend 2-3 months every year. Make that your︊ official base and sleep well at night. You can still travel as much as you︋ like. But you will have a proper home and everyone will understand that that is︌ where you should pay your taxes.
For a full PT-only lifestyle (with or without some︍ "artificial" residency), I wouldn't recommend you to spend more than 2 months in any country,︎ and even then there is some remaining risk.