The hotels are to some extent loosing out by not offering benefits. I'm a Hilton member. Booking through BAH I often have a Hilton amongst other choices. Not having the benefits means I have no incentive to book Hilton throuh BAH so they loose my business on those occaisions.

On one visit, Hilton booked through BAH, the staff who checked me in got out 2 bottles of water for me as a Silver member at the time. A second member of staff intervened and took them away. I emailed Hilton explaining how petty I found this. On my next stay I found a full bottle of wine and box of chocolates in my room