Or perhaps Dr. Piper from WNMHGB could take over. I wouldn't mind seeing Yeoman Colt return as well. Regardless, I don't think it is a problem of content but of interest. However...It is ultimately like most Star Trek shows. A ship and the crew, doing things. People already like the ship (the Enterprise) and the new versions of the old characters (Pike, Spock and #1) have been well received. They just need couple of more characters, Boyce maybe, unless he has retired, and some new ones which they can develop freely. Nhan could return to Enterprise, the character has gotten some developement and seems to be liked well enough.
You might be on to something with the nostalgia milking. I just think it will run afoul canonistas, though perhaps not any worse than Burnham has.It is true that having two 'ship shows' might be somewhat difficult to differentiate, but I don't see that as a huge problem. Maybe the Discovery could remain more modern and experimental series where they try new things and have serialised seasons, whereas the Pike show could be more traditional, episodic and fan-servicy for milking TOS nostalgia for maximum effect.