You are right about Van Halen being the godfather of cock-rock (along with KISS and maybe Def Leppard) and they did provide the blueprint for a lot of crappy bands. That doesn't lessen their legacy though. They made six classic albums with at least 20 songs that are classic rock staples, instantly recognizable to millions of fans. There is a world of difference between "Jamie's Cryin" and "The Final countdown." If you want to blame Van Halen for Trixter then you will also have to blame Pearl Jam for Creed and Nirvana for a lot of crappy bands that came out in the 90s/00s. A lot of punk/alt. rockers of the 80s/90s also grew up on Van Halen and Van Halen were the band that got them to pick up a guitar. The Minuteman have covered Van Halen, Pearl Jam have played "Ain't Talken 'Bout Love" a few times. Henry rollins is huge fan. What bands other than cock rockers of the 80s were impacted by Van Halen?
As for the Pumpkins, I'm a huge fan of
Zeitgeist, although I know a lot of people didn't care for it. I also have no problem with BC using the Pumpkins name, as he was their lead singer/guitar player, wrote almost all of their songs, played most of the parts on the albums, etc.