It’s the same as every time someone says that the airline is losing/going to lose some business by not affording them a flexibility when they need it on a non flex ticket whereby it is not owed based on the rules and the person could have booked something flexible: the airline may lose their business, but by enforcing their rules, they get plenty of others to pay more for a flexible ticket which they wouldn’t do if they knew they could get the flexibility without the price.

Hilton wants people to book direct. Sure, they may lose your business by not giving you perks when you book through bah, but by doing that, there are plenty of others who will book direct through Hilton which they wouldn’t do if they knew they could book in any other way (again the whole notion bah should get better treatment than Expedia or Priceline is a complete nonstarter, it’s all or none or some preferred partners only which would then certainly not include bah as they being in a tiny and unremarkable market).

in other words, if Hilton did what you said, they would add a fairly measly amount by getting whatever is left of your (and other similar) room rates after paying double digit commission to bah and whoever, but they would lose out far more by paying the same two digit commission on many rooms they are currently selling direct to platinum and diamond customers who know they have no choice but to do so if they want to get their perks. Considering most hotels occupancy rates these days, this is a no brainer. the calculation takes mere seconds to conclude that Hilton. Marriott and Accor will be very happy to lose those Expedia and bah customers to boost their proportion of direct sales.