Can government control buying most of the coins in the market?
I am wondering if your question is could the government buy up all the crypto that is in supply? to control or corner the market?
or
Could they control who can buy crypto?
The first one first?
They could try buying up all the crypto, and on paper it seems the sub $200 billion price might be a drop in the bucket, but I think as soon as somebody went on that kind of a buying run the price would soar. The market would react and the capitalisation would spiral to unimaginable highs. There would also be some hold outs - who under no circumstances would sell, they would do this on a point of principle, and then what would be to stop anyone/everyone starting new currencies to cash in on the bonanza?
The second question, controlling who can buy currencies? this is already partially the case in some countries - but its not fully implementable, because I could sell you some crypto coins over the internet, or in a face to face encounter and who is going to stop that? See Venezuala.