I think you're too optimistic about that. Those big players can easily sell $1 million worth of BTC within a minute or so, and I doubt the orderbook can absorb that volume easily. Sure, they can do it OTC, but when they do that, there's no guarantee that insider/the broker itself follows it by selling some of their money, so there's still a huge sell pressure.
Well, hopefully this hate and love relationship between institution and retail investors won't last forever.
1 million dollars is nothing, that is happens constantly, it happens so much that it happens probably nearly under 5 minutes each day, a million dollars is sold exact 5 minutes, it is incredibly common. You know why? Because we have over 33 billion dollars in volume, I do not know how they calculate it but that is over 1 billion dollars per hour, yes that is right over 1 billion dollars per hour.
You know why whales can't impact the price? Because they do not really have as much influence over the price with just their wallets. But do you know how they can? They can tweet about it and tens of billions of dollars worth of bitcoin all over the world will be sold, that's how. So it is not their wallet or basically their money that can destroy the price, it is their influence that can destroy it, all they have to do is say something bad and they would cause a huge crash.