I remember when WTAM had that reverb effect applied to their processing. WMJI even did this as well, though it was likely applied at the studio as it only affected the DJs when on the air.
I've noticed that WAKR AM 1590's processing sounds a bit harsh. As one of the few AMs left with a music format, I believe that their digital processor is not set correctly for music on AM, or that it can't replicate the sound or curves of an older analog processor. I have some tapes from another AM station that date back to 2000, and the processing sounded very good and pleasing to the ear. However, over the years, the frequency response slowly started to degrade, and it was likely switched out with a digital one in 2006 when the station launched their IBOC carrier.