I'd have to say Motley Crue getting a big hit with "Home Sweet Home" is the turning point where every hair band suddenly started having 1 or 2 ballads on their albums!
Actually... Twisted Sister had a hit with "The Price" in 1984 and Def Leppard had a hit with "Bringin' On The Heartbreak" in 1981....
But yeah Home Sweet Home was the BIG ONE! They had to change the rules of MTV's request show because that was being requested too much & overplayed! After that song is really when the power ballad became the ticket to success. Release a rockin' first single to get you on MTV and establish your sound and get known, then release a power ballad as the 2nd single and sky rocket into the top 5 singles!
I think with Def Leppard it was more a case of them wanting to me more of a melodic rock band than a heavy metal band. Their songs aren't so much power ballads as melodic rock tracks.
Yeah there were tons of ballads around before Home Sweet Home, but it was after Home Sweet Home that power ballads in hair metal became the trick to mainstream success & tons of bands were doing it!
Though Kiss had their biggest single of the vintage era with Beth as well... but the other bands didn't seem to follow that trend like they did with Motley & Home Sweet Home.
"Grinding makes so uptight
And you gotta face it, cause it decorates your neck
Its gonna stay there
Stay there for a long time
Just to remind you while you like it
When you went on and on
It hurts just the first time
Ooh, it hurts
It hurts just the very first time"