No they shouldn't put it to rest. They shouldn't have to. It's a good song, it's a successful song, they're still making money off of it, so why shouldn't they be proud of it? I got sick of it for a time too, a couple of years ago, but I got over it.
I know it has been used time and time again in movies and TV shows, and yes, Journey has to approve that... but personally, I find the overuse coming from other places.
Here in Chicago, ever since the White Sox thing, the newscasts use it as background for EVERY sport when a team wins something. I hear that song on the news no less than 3 times a week. And WGN (the worst offender of playing DSB) has expanded it to other Journey songs. When players are traded or on the injury list, they play "I'll Be Alight Without You". Once I heard "Stone In Love" but I don't remember what the point of that one was.
The damn Redwings have taken DSB also, because of the whole "south Detroit" thing. I've heard it every game so far.