You already do owe taxes... to some nation.
Presumably when you are doing business, you are the citizen of a country and a resident of a country. That country considers your activities to be taxable income in their country.
Sometimes this jurisdiction can be ambiguous, and countries have tax treaties to resolve that one nation taxes you, so you aren't paying significant taxes in multiple countries. (The US requires their citizens abroad to report foreign income, and in some cases pay tax on it. I suppose you could use this approach with the IRS and incorrectly file the paperwork as if you are a citizen). That will get you no closer to US citizenship.
Anyway, I'd really hate for you to cheerfully pay US taxes and then later, find you owe taxes to another country. As such, if you want to support the US, I say avoid a flat-out donation and simply file your 1040 tax forms incorrectly. That way, if things go horribly wrong, you can reverse it by filing a 1040X "amended tax return" with the corrected information. IRS will then send your money back to you (eventually LOL). Provided you file it within 3 years.
Note also that there are amazing American non-profits (not-for-dividend or NGO) organizations worthy of support. A huge amount of "what would be a government role" is done by nonprofits - from charitable support of the needy, to actual law-making. (Really. NFPA and UL are two public charities that craft almost all electrical and appliance safety laws.)
Denomination in dollars does not create US tax obligation
The US dollar has been laughably referred to as "the world's reserve currency" given the long-term stable status - not generally subject to national upheavals, hyperinflation and other maladies - and of course, accepted everywhere. A Serb doing business in Zimbabwe might use it rather than local currencies.
The mere fact of two foreigners doing such transactions does not create a tax obligation to the United States.
Conversely if myself and a person in Japan did business, and for whatever reason (supplier issues?) I was paid in Euros, I do not owe any tax to Portugal.
Who would I pay taxes to if I was doing business in Bitcoin? Sealand?
In fact, if you use certain freelance websites, you may be required to do business denominated in USD. But they will ask you all required questions to comply with US tax law. I doubt all such sites know how to do tax reporting in every country; they might simply refuse to do business with people in countries they are not prepared to do tax work with. I suppose you could lie to those sites and claim you are domiciled in the United States; that would create a US tax obligation until you showed IRS that you lied to the employer. (however this also means lying on the W-4 and other paperwork they collected, which may create other obligations).