Would Tim Allen still be as successful today if he starred in lead roles in movies during the 80s?

He could have been easily.

I don't see why  " The Santa Clause"  wouldn't work today as well as it did back then. 

In fact, I am surprised there hasn't been new sequels. 

Many popular old TV shows could not be made today because of "social awareness".  If you haven't seen "All in the Family" watch a few episodes.