It sounds like a perfect conspiracy theory to me! US is a free country and its citizens can start a legal business anytime they want.
Using the full power of the US federal government to give your business an unfair advantage by leveraging your position as president is not... a free market. Indeed it's the very opposite of a free market.
Bitcoin is far bigger for only US to control. Talking about competitor, Bitcoin has seen millions of competitors till date. No one was able to come close even by an inch. So bring it on!
If the US made Bitcoin illegal--and pressured it's allies to do the same--then yes, Bitcoin may well still "survive" in a technical sense.
But the price of Bitcoin would fall by 95% as the developed world's investors would pull out of it.
If you want Bitcoin to have a competitor in the marketplace whose CEO literally has control of nuclear weapons and the laws of the United States then... vote for Trump.