Then the US gov would have the ability to control the circulating supply of BTC.
Think of it this way, BTC caps out, then the US gov HODLed 50% of all BTC for an uncertain amount of time (call it a decade). The rest of the world starts to take risks accordingly and make investment strategies based on “no possible inflation, because BTC”.
After a decade+ of BTC HODL policy the US gov decides to release 5% it wouldn’t be “printing BTC” but it would still certainly be “quantitative easing” and the extra supply of BTC would result in very much the same inflation as we see today.
There is no scenario where the largest governments of the world cannot directly control the supply of circulating money! (Which is the only money that really matters).