Does the management really believe that the AM signal is worthless? If so, they could ask the FCC to delete the AM license and save big on the electric bill.
They don't sell any of their audience in Tucson, so they don't monetize it. They're obviously transitioning the audience to the FM, and at some point, sure they'll shut it down. But like most radio people, they're probably hoping to get credit for owning it towards the license of another FM at some point. Until then, they'll give the FCC a usable signal and annual license fees in exchange for the right to program the signal. They're a much better occupant of that signal than anyone else who'd get it.