I would in a lot of ways like a hard reboot of Trek.
I had a whole thread a few years back with my ideas of how you could modernize Trek in a full reboot. There's lots of more "modern" SF stories which simply can't be done in the Trekverse, for example, because the universe almost totally avoids transhumanist/posthumanist themes.
That said it has to be noted that when other IPs are rebooted, this is often due to the appeal of the
core characters. On a fundamental level, I don't think Kirk (or anyone else) has that sort of transferrable cache that Captain America, James Bond, Sherlock Holmes, etc. have. The appeal of Trek is built into it being a good framework for exploring the human condition through a SF lens, and it can use any characters to do so. There's a strong argument to be made for this reason that if you mess with continuity a bit too much it raises the question why you didn't just create an entirely new IP.