They already have that option. The point of contention is that the city wants to include BAS/BAQ in calculating their military pay scale.
Does the city pay for their officer's homes in the U.S.? If not then how the hell can they claim that housing is part of the pay for troops on active duty? It's more of a necessity than a perk?
Military life isn't like life in the private sector. Those troops are on duty 24/7. Instead of working a 40 hour week, they are on call at a moments notice.
Tell you what, if the city wants to buy each officer a new home of their choice in the U.S. upon return, perhaps I'd ammend my reponse.