If your conclusion about daytrading stocks with buying power in excess of $20 million is correct, then another valid conclusion would be that hedge funds also trade longer timeframes. However you failed to mention this as a possibility.
This thread is too long to read....but all I know is... If you have $20mil+, you don't need to trade. Actually you don't need the market period! You have the luxury of waiting for mass-panic bottoms like 1974, or end-of-the-world atmospheres like 1932. Can you trade $20mil? sure.... but you're missing the larger picture.
Can easily trade $20 million in equities, though really is a function of leverage and desired return on capital. If offered 10:1 leverage on $2 million, that's $20 large, minus the margin charge. As liquidity is a necessary prerequisite, otherwise slippage becomes a real haircut, IMHO best to trade black box spreads of at least 50 to 100 NYSE listings. If flat rate commission, returns can be stellar. How much? 200% to 500% per month on original capital, i.e., the $2 million and so on, as per each month's starting equity plus profit additions. Not a bad progressive pay day, year in, year out, other than short term capital gains tax unless trading for non-USA client(s) offshore. Now, want to trade someone else's $1 billion for a 25% of profit cut per annum? Not out of the question . . . in fact, it's reality.
you could do one heck of a great big HFT ratio trade with the full s&p contract with that kind of money --- that would be fun.