I like Sammy Hagar as a singer, but I thought Van Halen became too ballad-y when he took over.
I absolutely cannot see David Lee Roth getting up there and singing most of their hits after he left the band. I can't hear his voice on any of those songs in studio either. It would just be really weird.
Then again, I can kind of hear him on Right Now, Top of the World and Finish What Ya Started.
I can't hear him on hardly any of the 5150 songs or most of the others that I didn't name. I'm laughing thinking about him singing When it's Love, Why Can't this be Love, their message in a bottle song, etc.
Conversely, I could imagine Sammy Hagar singing most of the David Lee Roth songs, other than some of the goofy ones like Hot for Teacher. Ice Cream Man, Just because he was more versatile. I definitely like David Lee Roth Van Halen better though.