Yes, it is possible for foreigners to have/keep a US bank account*.
For the remainder: IANAL (nor tax advisor), and have never been resident to the US. So everyone, if my guesstimates are off, please let me know.
I have a US bank account which I opened as a foreigner with tax residency somewhere else.
I regularly hand in forms (via the US bank) that I have foreign status and where I'm tax resident, i.e. which double-taxation treaty applies for me. The bank then deducts e.g capital gains taxes according to the tax treaty and sends me a tax certificate that I submit with my "home" income tax declaration.
I'm not going to pay taxes as I'm not resident.
My guesstimate is that you are going to pay taxes: the bank will automatically subtract them (at least that's what my bank does). If you have your tax residency in a country with whom the US have such a tax treaty, you're paying lower US taxes (and they may be accounted as taxes already paid by your tax residency country - all this depends on the particular tax treaty). If not, you'll be paying full taxes.
Income tax (and sales tax) for digital nomads is difficult: the laws can differ widely from country to country.
If we're talking salary, the country of the employer will be important: at least a whole lot of European countries I'm familiar with will have the employer make automatic withholdings. If you're not resident there (which you'd show by establishing where your tax residency is)
If we're talking freelancing/your own business: Things may get complicated as strictly the country where you are when doing the work is usually(?) the country whose e.g. sales tax is due, and there are countries that say income generated here are subject to our tax (and be careful what your visum allows).
What I've encountered when working with foreign customers at their place: you may need a sales tax number there, or the customer can take care of that for you. Some countries allow a flat taxation of what sales you made there. In any case, the declarations I've met so far ask for your tax residence. If you don't have any, you need to have one of their tax numbers. Guess what that means? Doing tax declaration there in addition.
Nowadays, even if you as a foreign seller sell via a marketplace like Amazon in my country, you'll need a VAT number here.
For digital nomads, there are discussions in the internet whether (how) one can be "tax homeless" and thus not subject to income tax anywhere. However, e.g. my home country says that commercial income generated here is subject to income tax regardless of whether you are tax resident or not. If you are tax resident here, you have better conditions in terms of what you can deduct, so income tax being due but not being tax resident can very well mean that the income tax due is higher.
You may think that anyways noone will notice: but at least over here B2B customers wouldn't consider you if you don't have a tax number and proper address (and if it's a tax number that says your VAT exempt) - otherwise your bill is not considered proper which has consequences for their taxes... And private customers would be very careful if your business doesn't have a proper address.
* I don't know whether there are trade embargos for particular countries in that respect.