Hotel room cost is one of the largest individual expenses I see come through for Federal travel. There is currently no incentive for an employee to stay at any place charging less than the maximum per diem.
I suggest that if the traveler stays at a hotel with a rate lower than per diem (or even stays with a friend/relative), then the traveler should be allowed to split the cost of the savings with the government.
For example, if the per diem rate is $75/night, and the traveler stays at a hotel for $55/night, then the traveler gets a "bonus" of $10, and the government saves $10 off what it could have spent. Both sides win. If an employee wants to stay at a fleabag motel in order to save money, there is an incentive. If an employee wants to stay at a Marriott property, then the per diem will still allow it.