I like the flexibility of the cast idea. Not sure about the time travel though. It's alright in small doses, but not sure about a full Trek show about it.
I think the main problem with time travel in Star Trek was that good use of time travel was underdone, while bad use of time travel was overdone. It has always been an opportunity to explore something great, from moments of Earth's past, to the history of the crew to unconventional story lines, but that opportunity has been missed, and then utterly ruined by the temporal cold war which revolved around “OMG TIME TRAVEL!!1”.
And I would much prefer to see such stories done in Star Trek fashion, not Doctor Who fashion, because Star Trek's take is more serious. Sometimes way too serious though.
But if there was a story type I would like to see more is undesired contacts with 20/21st century-level societies with accidental prime directive violations.
But only if they are done well.