No.
I have three theses.
1. In part, hair metal never died until the mid 90s - 2000s.
This is a radical thesis, but arena rock bands continued churning out multi-platinum albums.
-Guns and Roses were huge, and sure they were wearing flannel shirts in 91-92 but it was still glam rock. Most of their 90s stuff was written in the 80s anyway.
-Van Halen went three times platinum in 91, and then again in 95, and they were still doing rockers to open their albums and power ballads.
-Aerosmith's Get a Grip was another hair album which was wildly successful in 93. They pretty much released the same crap in 97 and 02 and went multiple platinum. The sappy ballad "I don't want to miss a thing" was huge.
-Mr. Big and Firehouse still had top 40 hits in 1995. This proves that people were still into the sound--however, they released sucky albums and otherwise made no sales.
-Kiss kept selling albums other than the trend jumping carnival of souls--in the 2000s, the obvious glam rock song "live to win" did very well.
-def leppard did well in the early 90s, but i must admit their 97 album was pretty solid but didn't sell. by then, the genre was starting to peter out.
-Damn Yankees did great in 92, but then broke up. However, this shows the strength of the genre at this point.
2. Top acts trend-jumped when they probably did not have to in order to remain commercially viable.
The above shows that name-brand acts still garnered mainstream radio play, mtv waterchers, and record sales. Yet, they all still made hair rock. However, the following acts trend jumped when they could have easily towed the line and made money--
-Alice in Chains went from metal to grunge. Their first album was headbangers ball stuff, and even the B-side "Fear the Voices" made in 1992 shows they were still making hair rock--but dumped it for marketing reasons and Cantrell's own eccentric (and excellent) taste. However, being that "Face Lift" towed the line between arena rock and the seattle sound, they could have easily continued to do so as the audience was there.
-Metallica went from the pinnacle of success arena rock with the black album to still very successful Grungtallica (and then Nutallica.) If they released material like the black album, it would have easily still went multiple times platinum.
-Ditto for Megadeth, though I would miss the song Trust
-Bon Jovi went from hair to adult contemporary (keep the faith) to listless-youth oriented rock (their unknown 1995 album) back to hair rock (it's my life, have a nice day). Ironically, they were still getting mainstream play in the 2000s. The local high school in my town had a have a nice day bumper sticker on the stop sign. these 40 somethings still had teen accessibility. Bon Jovi might have been bigger if they just kept up doing arena rock albums, as that's what they ultimately reverted to for their singles.
3. Really crap luck with the next generation.
Hair rock died because some bands got way too old (Aerosmith), broke up (Van Halen, Damn Yankees), and trend jumped. However, how about those that didn't?
-Guns n roses simply stopped making albums after they churned out arena rock covers like live and let die in 93.
-Skid Row simply did not have creative talent to continue...a bon jovi reject was simply not enough of a creative force.
-young bands like faster pussycat, white lion, cinderella, warrant, slaughter, and winger made bad follow up albums after 92, which ensured that there exists no vibrant core of bands to keep the genre viable and thereby encourage other bands to follow suit.
In the end, arena rock outlived grunge.