Could the Fed hoard Bitcoin?

Hear me out:

With the possible future introduction of CBDCs, do you think those in power would push these government shit coins to the public, all while claiming Bitcoin is dead/inferior, etc. but secretly stockpiling cheap Bitcoin?

We've come to see how slimy these fuckers like Klaus Schwab can be. I can see the government officials spreading FUD about Bitcoin, making the average joe second-guess it, sell it for CBDCs, driving BTC's price down, and allowing higher-ups to pick up more of it for cheap.

Think about history - in 1933 the Federal Reserve called for Americans to give up their honest money (gold) for fiat shit (US dollars) while the Fed hoarded more and more sound, hard money (gold), giving them more power. They can't necessarily do that with Bitcoin, but they could try to part people with their BTC through FUD, misinformation, MSM propaganda, etc.

Then, when those in power have sufficient BTC, they switch their stance and make BTC legal tender, maybe the preferred tender, and now the average joe has to pay a fortune for a small amount of sats. I'm just theorizing here and fishing for discussion. So, any thoughts on this?