It's actually the other way around. As a big fund looking to trade a large number of shares in the public market, you'll quickly realize that the market tends to move away from you, and statistically, you're more likely to get a bad deal than a good one. Even if you try to be smart about execution by splitting your orders into chunks, randomizing order sizes, and similar tactics, there is still a huge information asymmetry between you and more sophisticated players. In many cases, they can classify your orders based on different characteristics of your order flow (such as latency profile), distinguishing them from so-called toxic flow from other HFT firms.
The purpose of these private rooms is to separate your orders from those players so that you trade against other uninformed parties, making your chances of getting a good or bad deal closer to 50/50.
The purpose of these private rooms is to separate your orders from those players so that you trade against other uninformed parties, making your chances of getting a good or bad deal closer to 50/50.