The old (or: original) Alice Cooper Band had something dangerous, garage, edgy, underground and at the same time carefree. Add those early Zappa influences. They were more MC5, Doors, New York Dolls or Stooges than, say, Grand Funk Railroad, Aerosmith, Kiss or Foghat. To be fair, even the original band already began to lose that somewhat around Billion Dollar Babies. And the Jack Douglas-produced Muscle of Love that followed was perhaps already a bit too much in the Aerosmith stadium rock vein (though still a solid rock album), the Alice Cooper Band had left the garage for good by then and Alice had gone for a stroll to the golf course, unfortunately he never returned.
Everything concerning Alice that came after (and there were some great, even superior musicians involved) was/is just an - entertaining - Vaudeville show. More Addams Family than a society question mark. He has become the Vincent Price of rock when perhaps he could have been Dennis Hopper - he wouldn't take that as an insult either, he is a creature of his own creation.