Also, maybe some stations don't want it widely known that they are not live and local. A dead giveaway used to be the old "xx minutes past the hour" time checks, but come to think of it, I don't recall Jeff Rollins and company giving any time checks any more. (I could be wrong -- I just haven't noticed).
On the other hand, most listeners anymore probably wouldn't care whether a station was live and local given the trend toward jockless music stations.