If I was in their sound department, I would have a Michael Anthony vocal track on every song, which I am sure they own. I never had proper respect for Michael until I saw a Chicken Foot concert, not only can he sing but he has the groove to keep up with the best in improvisations. Considering the multi musical generations and gene's of the Halen's, I imagine Woolf is as good or better technically than Anthony was at this stage, but M.A's piercing harmonies are instrumental in reproducing the aesthetics of early Van Halen.
I think the bass solo from the 1st Van Hagard VHS concert hurt his credibility. Not sure whos idea it was but it was basically a feedback laden effects free for all triggered probably by Eddie backstage somewhere.