So, you would be open to rebooting Indy with a new actor? An interesting thought.
Sure. Why not? Some day they will make another Indiana Jones movie. It might be a REALLY long time from now. Who knows?
They're making more Perry Masons. They just made an inexplicably old Philip Marlow.
Characters that have multiple stories can / should have multiple actors. It's only because it's FILM that we think "Nobody can play that part ever again." I mean, someone can TRY to make Casablanca again. I wouldn't advise it. But if they do not having the CG-reanimated corpse of Bogey will not be why they have a problem.
So far I have not been impressed with Paul Wesley not because he's not Bill Shatner but because he's not (so far) a very good James Kirk. (Fingers crossed for S2.) Chris Pine is an amazing Kirk. I really really enjoy Peck's Spock. And Mount is my platonic ideal of a starship captain at the moment.
The one tiny niche carve out exception I've thought of is Rogue One. Because it's really supposed to be the long prologue to Star Wars. It's a kind of magic trick. But it should be the exception not the rule.
OTOH, I think they absolutely should have recast Carrie Fisher for The Rise of Skywalker because not doing so hurt the story and the character. It was to be Leia's movie the way The Force Awakens was Han's and The Last Jedi's was Luke's. We're sorry that Carrie wasn't around to see it but sorrier still that neither did we.
Watching The Old Man with Jeff Bridges and John Lithgow I might consider for a moment that the actors they have cast as the "young" versions are not what I remember these men looking like in the 1990s. (Well, the Bridges character. The young Lithgow is SPOOKY.) But after that I watch the show and count my lucky stars that they didn't try any CG trickery.