As a government traveler, there is a maximum rate for lodging allowance, and people will often book a hotel at this maximum rate (in fact, in places like Honolulu, all the hotels know the max rate and will charge the travelers that amount).
However, sometimes the traveler has family or friends in the area and would enjoy staying with them instead. Allowing the traveler to opt for 50% of the max as an allowance on their travel claim would incentivize the traveler to stay with friends/family and save the government a lot of money. Notably, in the Hawaii example, the government would allow the member to opt for $85/day in cash rather than pay a hotel $170/night. This "max" frequently doesn't include such add-ons as tax & parking, so government savings would actually go over 50% when this option is utilized.
In addition, a person could nontheless stay in a "lower quality" hotel that costs less than 50% of the max and pocket money in that fashion instead.
Essentially the system currently incentivizes the traveler to maximize the cost to the government where the government could be saving money by incentivizing the individual to seek personal gain.