If you are US citizen you are subject to US income taxation wherever you live. No matter how long you live there. Even green card holders are subject to the same rules as citizens.
How is a country you plan on visiting going to know what you are doing, other than visiting, while there?
Citizens of U.S. territories have their own tax rules. It's the only way to avoid the IRS while maintaining U.S. citizenship. I think I understand the U.S. rules. I know I owe taxes to the federal government as long as I'm not a resident of one of our territories. I'm more concerned about foreign countries trying to tax me than I am about here.
With different timezones that might not even work in other continents expect the Americas (assuming you are trading US markets) eg here in the UK co working spaces are not 24 hours, only business hours, which are obviously not the same as US business hours. For 24 hours access you would need a rent a more expensive dedicated desk and if in Asia turn up in the middle of the night. Trading while gallivanting around world works best when trading with an automated system.
Most traders don't pay taxes (because they don't earn money). A few traders are earning tons of money. They are more than happy to pay taxes. They don't waste time avoiding paying taxes.
For me personally, this is just nonsense. Almost all the money I've earned in my life so far has come from trading. Income fluctuates drastically year to year. If you're bringing in mid six figures one year you're paying six figures in taxes. Then you can have a shit year where you're flat or lose a little and pay little to nothing. If you're trying to build wealth taxes slow you down a lot. I get that taxes are necessary, but right now I'm trying to build wealth so I can be financially free and never have to worry about working a "real job". I don't know the prospects of this for a living in the long-run. AI might takeover the game completely and leave little edge. I have to make now while there's still opportunity.