What you're saying is that Bitcoin markets is illiquid. That's something I can understand and perhaps even try to give a reasonable answer to.
That "network transactions are so backlogged that it's an illiquid market" is not. (Backlogs doesn't make for illuquid markets, and even if it did it doesn't affect the "big players" at all.) Trading on exchanges is off-chain in the sense that no transactions takes place on the public blockchain.
Bitcoin markets used to be rather thin, but volumes haven't dropped in proportion to rising value. Which is to be expected with a more mature market. Your specific example of a million (US dollars, I presume) would hardly be noticable on any of the big exchanges today. That's just 500 bitcoins. I wouldn't worry about it.
Keep in mind that Bitcoin is still inflationary and four times that amount is mined every day, most of which is sold. That's just what's visible, and who knows what's going on off the order books.