He writes over chords, and simply doesn't have linear melody lines that are hummable and memorable. And, he destroys any chance at remembering the songs by drowning his melodies in a wall of sound, the guitar jangle obscuring anything else, such that each up-tempo song is just non-stop jangle and they all sound the same -- and the slower songs get pretty dull.
Huh? I'm not sure what songs Elvis was singing, but I've never felt that from Costello's music. Think about the memorable tunes from Costello like "Oliver's Army," "Alison," "Tokyo Storm Warning," "New Amsterdam," etc. Costello is one of the finest songwriters America has ever produced. Albums like My Aim Is True defined the direction of alternative music, yet was able to infiltrate the mainstream radio. Costello is known for nothing if not creating melodies that infect the mind of the listener and leave you humming the song later that day.
Perhaps Costello was just singing newer stuff from North that are less like his signature sound. I wouldn't think he would have a concert where he didn't sing at least a few of his hits. I hope that Jeremy at some point can hear some of Costello's music in a more laid back setting. Perhaps he'll see why so many people love Costello.