I think it's more just that he's kinda awkward. I remember Ken Caillait or others saying he's just not really a people person and is just naturally serious. So he's probably just not super comfortable on a red carpet.

Maybe.

I think he's just afraid someone might get the mistaken impression that he's into the "fame" thing, that he's courting fame. Stevie makes no bones about it, but Lindsey has always had an uncomfortable relationship with the 'fame' and 'star' thing.... always wanting it to be about the art. He seems to have at some point since like The Dance embraced the being a "Performer" onstage but he does resort a bit to the "artiste" thing onstage, at least at solo shows. But at solo shows he's still more of a mix of Performer and Artist now than he used to be.

I don't think that particular thing is on his mind on a red carpet but I agree, I think he always wanted to be successful in the realms of those big famous musicians but he never really wanted/cared to be the 'celebrity' that they were.