This is not true. Liquidity in these markets is steadily increasing. It is easier now to sell large amounts of Bitcoin than it was two years ago, and it was easier then than two years prior.
A million dollars perhaps used to be problematic, but is now a drop in the bucket on any exchange's daily volume. A normal bank transfer will suffice, but check with your bank if you aren't moving those amounts regularly. For bigger volumes there is a quite functional OTC market as well.
These types of investors also panic easily, once the bank run starts, nobody will be buying. In fact, I bet most exchanges will simply close up shop.