Now, a very common logic, which institution would like to buy btc at $100k or even at million dollars when the seller institution is already taking out big profits in fiat by selling their btc to the buyer Institution? Won't that btc be coming with an impermanent loss if the price dumps later? Do you think there is any point where a stagnancy of liquidity or financial crunch may affect the price of btc so badly that it can reverse down like it did in the 2018 crash?
One thing to mention about here is Bitcoin won't reach 100,000$ "hypothetically" if there is no demand pushing it to do so, Bitcoin going up to that value means there was a sudden increase in demand even though it went up. Your other problem with regards to them selling their cryptocurrencies it will always be a double edged sword as they can sell it all at once and do a short but in this strategy they wouldn't be able to sell all of their holdings at the highest possible price as they have put a lot of pressure on the sellers' side so the most smart thing for them to do is to sell it in trenches for them to maximize the highest profit possible while not influencing the price of Bitcoin.