If created and developed properly, the focus and "hook" for a new Trek series should be the characters--who they are as individuals, how they interact with one another, and how they react to whatever situations they encounter.
With an all new crew you can do whatever you want with them (within reason of course).
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)