Why would they acquire it just to take it off the air, unless you mean just go off the air at night (that's what I meant by "become daytime only").
At night it has to protect stations in NJ, upstate NY, and elsewhere. The station was a non-directional 5,000 watt daytimer only until the late '80s, when it added extremely directional 1000 watt night service, aimed mainly toward the North Shore and the north suburbs within Route 128. It isn't allowed to send much power anywhere else. The night signal only reaches the parts of Boston and nearby points south that are right along the coast, carried over the water.
If they're really ambitious and have some money, I wonder if they could build a directional site somewhere southwest of Boston, and send more power northeast from there, covering more of the greater Boston area while still protecting the NY and NJ stations?