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?
Something we haven't seen before, new characters and situations for a new generation like TNG was (the same question was asked of them, but it's also asked of every
new TV series with new characters).
A case could really be made that there was overkill after TNG with too many Trek shows coming out on the heels of one another (if not stepping on one another's toes). Had it not been UPN, VOY and ENT wouldn't have been made and there might have been a good long while without a Trek series after DS9 (it's even conceivable that we'd only now
would be in a very different Series IV in such a case).