No they can't. The moment they start doing this, it will rise the price of Bitcoin, but mostly because their fiat goes down the drain. Look at my country, 6 years of infinite "printing", and its now one of the poorest in the world thanks to that policy.
IT DOES NOT WORK.
You propose as "solution" to do the same, but you cannot be more wrong. The solution is actually what Bitcoin already is, a finite supply. Or why do you think no single entity owns the entire world's gold reserve?
Some people with naive socialist thinking, believe the market can be easily manipulated in this fashion, yet they always find the hard way that no, it doesn't. Their problem is they see the market as "unfair" and believe their direct manipulation can "correct" this "unfairness". In reality, any type of State intervention produces an even worse unfairness. The State is simply another big entity trying to manipulate things, but failing to do so. Implement policies, prosecute people, they can't stop it. Market will rebuild itself and reroute around any obstacles, just like Bitcoin does in countries where its "banned".
All of human history is filled with markets, and people foolishly (monarchs and other autocrats) trying to control them, resulting in utter failure always.
You see, the moment new fiat appears out of nowhere, the price of the thing you intend to buy has already changed.
Furthermore thanks to the infamous 51% attack, the goal isn't even to buy all bitcoin but 51% of it, and yet no entity has managed to do so, and never will.