I largely agree with that idea. It feels like at some point Trek will need to let go of all old characters, to ensure its long-term viability. Personally, I'd be happy to get to know a new group (crew) of characters, even if they're not a famous character's offspring. I guess that was the idea with Discovery, but the universe/story arcs that they created didn't interest me too much.
I know that's not really how shows work, people get enamored with the cast and roles, but I'd love to see a semi-regular shift in crew or ship, while the writers tackle the issues of the day allegorically.