Haha! I’d forgotten all about that one. It’s original gems like these that folks who don’t know anything other than Weird Al’s most popular parodies need to hear so they can realize how oddly insightful his songs can be from time to time.
Since you been gone is another great one with a punch 
So, are you talking about criteria that you think should be there to be allowed in a Rock and Roll Hall of Fame, or are you looking at the actual criteria as seen by who’s already been inducted?
I mean, is the History of Music completely changed if John Melloncamp doesn’t exist? Doesn’t “fluff, like cultural wallpaper” describe KISS pretty well?
The first “Weird Al” record came out 31 years ago. People who grew up listening to his records are now well in to their own careers. Tenacious D, Flight of the Conchords, The Lonely Island all cite Al as a major influence. Their are many other artists that are loved by comedy music fans, I’m pointing to the “Big Three” that are known beyond fans of the genre.
Why do pretty much all of the most well-known comedic musicians avoid doing song parodies? Because Al has pretty much sewn up that entire thing. There are other parody artists and they all get the same question, “Oh, like “Weird Al”?” It is the lack of well known parody artists that illustrates Al’s immense influence.
I do comedy music, I don’t do parodies, and I still get asked “Oh, like “Weird Al”?”
The other reason the artists who cite him as an influence do not do parodies themselves is because, like most serious Al fans, many of their favorite songs are Al’s original songs.
Al has had plenty of influence.