At a certain point, it won't matter how much cash can get it. Either the dollar will die, or we'll get a cbdc that can't be traded for bitcoin. Then, companies and individuals will start trading equity and assets for bitcoin, and that will support the price.
Discussion
Their best route to control this thing is the drain the spot market completely, kills all the exchanges.
The price setting mechanism then becomes CME futures and "spot" ETFs. Both are cash products that have no settlement to BTC. Same way they controlled the gold market through GLD and silver through SLV. Not sure that will work but that is the playbook.
The problem with that is that if the States continue to decree gold, silver and bitcoin legal tender, they won't be able to control their distribution into the economy, which will increase the demand for them and weaken their control systems.