Robert Goulet died at age 73. I think he was one of those performers who went from being an easy target of mockery to being appreciated again.
As the obituary makes clear, he had the misfortune to come along just as his kind of singing was no longer making the charts; what it doesn't quite make clear is that Broadway also was moving away from his kind of singing. The big baritone voice had been a staple of Broadway musical theatre for decades; musical-theatre heroes were generally handsome guys with well-produced voices like Goulet's. Some of these people became stars, like Alfred Drake and John Raitt; others weren't big stars but worked a lot, like Bill Johnson or Ray Middleton; but strong baritone leading men were always in demand. But My Fair Lady had popularized a move toward casting non-singers in leading musical roles; amplification was coming in and changing the type of voices that were needed and wanted on Broadway. What all this means is that while Goulet did get a few other big Broadway roles, like the lead in The Happy Time (with a score by Cabaret's John Kander and Fred Ebb), someone with his particular talents would have gotten a lot more Broadway work even a decade earlier. Vegas was really the only place for him to go with any regularity, which is why I think people eventually came to understand that it was unfair to mock him, or other entertainers, for gravitating to a place where their style of singing was still popular.
A YouTube search for the phrase "Robert Goulet" brings up 165 videos, a testament to his continued popularity. Here's one of my favorite finds, Goulet in an episode of the '90s Disney Saturday morning cartoon "Recess" where he's the singing voice of the fat kid (in the inevitable "schlumpy kid has unexpectedly great singing voice" plot).