If a lot of companies who performed an ICO would actually cash out ether prices would tank pretty fast. There are a couple of paragraphs in the very recommendable Crypto Trader Digest (written by the people of BitMEX) which goes into a little more detail. Liquidity is still very low on all these exchanges so it doesn't take much for panic selling to set in.

I think a lot of money going to these ICOs are people that got into bitcoin/ethereum early trying to diversify their gains with more crypto tokens. Like, the BAT token consisted of 4 whales

its in ETH, not dollars, so it would be quite difficult to convert without slippage because the markets are quite illiquid.

Basically, people trading their ETH paper gains as a diverisification play.

ETH is not illiquid per se. Those ICOs just happen to collect 0.1% of all the circulating ETH, imagine you would go to a stock broker with 0.1% of all USD circulating...