Just think of the possibilities! We can have all our favorite characters in any story,
It would probably be best to start a show with a ship and half a dozen new principle characters.
Cameos of older characters are really dependent on a story that can bring them in.
Just because you have access to all of Star Trek's characters doesn't mean you use them all.
An audience would be totally confused.
Of course if you wanted to have Data or 'The Doctor' EMH Mark IV it would be pretty cool as they aren't human and could easily be in a wider year range of when a show is set.
And those two actors may even be willing to do the voice performances if the budget allowed.
[And we would also get a thin faced
Data like TNGs first few seasons.]