I don't think there are any rules here. There are examples on either side of the equation. Hell, people (in my opinion wrongly) call Kiss a "cover band" for having Tommy and Eric in the band. I have NEVER, EVER heard Tony Iommi called a "cover band", even though for most of the latter day period of the band, he was the sole member.
I think singers are important and in many cases, the singer can carry the show. Roth, Gabriel, Sting, Ozzy, Dio. And for every one of those, there's a singer that didn't light it up while solo. As much as I love him and his work, Dickinson's solo career is too much like him, all over the map. Halford did not light it up as a solo act. Tony Martin. Jon Anderson. Even the great Stephen Tyler is seemingly lost without Aerosmith.
And vice-versa; AC/DC and Van Halen thrived with singer changes, but Maiden and Priest did not.
I personally liked The Shattered Fortress (even if it was a constant slap-in-the-face reminder of how friggin' good James LaBrie really is). I'd go see the Circle - Sammy Hagar playing songs from his and his bandmates career - in heartbeat. I saw and LOVED the Chinese Democracy Guns 'n' Roses when I saw them in a 1,000 seat club. But honestly, I could care less about any of the 80's LA bands that are presently touring with singers they found on YooToob. I can't stand Vince Neil, but if I'm going to see Motley Crue, it will be with that fat ass barely scatting through the words, not John Corabi.