When large operators reduce their payloads: they carry out transactions not in rexchanges but P2P. Nobody wants to exaggerate the market by buying hundreds of millions of coins just to be dumped by the bear. If you exchange 1k or 10k bitcoins at once, the price will suddenly surge in the opposite direction (even if the position will soon be filled by the bot). No idea how much will be exchanged to fiat in "blackmarket" or alternative routes. Yes they would not buy Bitcoin in a single shot but they would buy it through a systematic investment plan, focusing on buying smaller units at higher frequencies.