Every time someone asks the question whether there should be yet another spin-off with a "new crew" - another question needs to be answered first.
The concept of the "TOS crew" have been there and done that for 50 years, what could an unknown set of new characters possibly have to offer?
A TOS/nu-trek script can easily mandate that Kirk and the Enterprise enters different galaxies, universes, time travel, get into war and conflicts, resolve them, and discover new life and perspectives and better themselves week in week out.
This is the scope of Kirk and co in Star Trek, there is no limit to what adventures the original crew can get into.
It is a winning formula, why anyone would think another Tom Paris, Harry Kim or Quark emulating what the TOS crew did would work I will never know.