I think remakes can definitely be worthwhile and even potentially outshine the original, though its rare to find examples of that. My favourite remake is Battlestar Galactica, my second favourite remake is... I have no bloody clue. A Fistful of Dollars maybe? I'm genuinely struggling to come up with remakes I've enjoyed. That Jim Carrey Fun with Dick and Jane remake in 2005 was watchable, so there's one. IMDb tells me that True Lies was a remake, so add that to the list I guess. Oh and Star Trek: The Motion Picture is a remake of The Changeling.
Things like Romeo and Juliet and Batman are closer to being adaptations, even if the only thing Batman keeps adapting is that bloody scene in Crime Alley with the his mother's pearls falling to the ground. I'm glad we're not getting that in James Gunn's new DC universe because we don't need to continually revisit the same part of the story in new movies when all the other adaptations still exist and there's so much more there to adapt.
I've certainly got other reasons why I don't want to see TOS in particular being remade, but I'm not all that eager to see anything being remade. Experience has taught me that most of the time it's better just to watch the original.