Exactly .... give room for new roles and characters to up and coming new actors.
William Shatner was a minor actor in the 60s until he became Captain Kirk ... same with George Takei, Nichel Nichols, Leonard Nimoy, DeForest Kelly .... their participation in Star Trek established their careers.
I love the new Trek because it keeps introducing us to new faces and new personalities that we've never seen before.
Cage has already done lots and he'll probably keep doing more because of his already established fame. He doesn't need to be on Trek .... maybe a short cameo but not a main character.
While not as big as your examples, I think Matt Frewer is similarly affiliated and his TNG episode turned out ok. I think it could be done, with the right script.
I agree the script matters and maybe it could be done without being sucky. Not that I don't love Cage but... I think Fewer is a bit better actor. Maybe not to quite the level of disappearing into the role like some do but still.
I think Michelle Yeoh was pretty well known by the time Discovery arrived and beyond initial recognition I kind of forgot all about who was behind the character. Likewise I forgot all about Whoopie Goldberg, it was just Guinan. (Maybe give Cage an iconic hat? Lol) David Ogden Stiers did well right? (I don't remember that episode very well).
I'm not sure if it would be as easy to blend Cage into a show.