Most States Exempt Federal Employees from paying state taxes for hotel accomadations; if you present a state hotel tax exemption form at the time of check-in. There is no requirement to ask for the exemption, and finding the forms can be difficult if you are travelling out of the state you are based in.
The Office of Management and Budget could require that all travellers submit a tax exempt form for hotel stays. They could make each state's tax exempt forms available on their website- enabling all federal government employees access to these forms. Making state lodging taxes ineligible for reimbursement if the form was available on the OMB website would save the Federal Government several tens of millions of dollars per year.