Every American is automatically a registered tax payer. If you work, they register you to pay taxes. The IRS has a rule stating that, if you are an American, and you worked last year, you owe taxes, no matter where in the world you live. They will consider the stocks and bonds, etc. in the other countries as your way of cheating them out of the taxes that oyu owe them, and they will prosecute you in court if you do not report it on your W-2, and do not pay the tax they tell you to pay. That's what happened to Charles Wrangle. He was censored in Congress for not reporting his rental property in Dominican Republic.
allowed to manage a stock brokerage account,
You don't set-up a brokerage account with an American broker without supplying them with your ssn. You make any profits, you will get a 1099 from the broker. These will also be reported to the IRS.
You make your profits in the US, you pay taxes here.
Am I, as an American citizen, although not a registered tax payer, allowed to manage a stock brokerage account, set up in a country with no capital gains tax or income tax?