What is the point of bidding if you do it at market rate or above? For that you can simply go to an exchange...
If i had the money, i would do the same: Bid at lower price than market, else its pointless.
Slippage. That's the whole reason many go to OTC trades.
No way could you obtain several thousand BTC in one go without risking driving the market batty. You could try it over a few days but even then others may notice strong and sustained buying and raise their sells.
Paying slightly above market for a one time buy could save you money vs buying on the open market.
I love a good bargain, and your logic is solid during flat and Bull markets. In a bear market you can find plenty of bargains without help from the Feds.