There's no way to tell if overexposure hurt Trek considering that for many years, it stunk and that could explain the dive in ratings/box office. If VOY, ENT and the last couple TNG movies had all been great or even good, and they were unpopular regardless, then yeah I might blame overexposure.
My hunch is that a really great Star Trek series would get strong ratings regardless of whether the franchise is overexposed, especially if it appeals to a whole new audience, which it really needs to, since there's no Star Trek TV channel.
Wherever it ends up, that channel will have an audience who the show must appeal to, and nobody should assume that audience overlaps to any great extent with the existing fans, just as JJ Abrams didn't assume his movie could be a success appealing only to fans.
So if Star Trek has to cultivate a new audience in order to survive, either in movies or TV how is overexposure even an issue? Most of those people have little or no exposure to Star Trek. It's not overexposure that hurt the franchise but failure to adapt with the times and also not to suck.
Keep in mind, tv-shows are not doing all that well these days. Most shows get cancelled pretty quickly. Mostly because people don't like to invest a lot of time in getting to know characters, follow long story-line and keeping focused. That's why movies work. It take 2/2,5 hours, and you're done. That's what people like these days, things that require less effort. Sad, but true.
TV shows have always had a high cancellation rate. Overall, TV viewership has not dropped, it's just being spread thin among more outlets than ever.
What's been happening lately is that TV is splitting into two camps. The episodic format that you describe belongs to broadcast, which is hostile territory to sci fi anyway, especially sci fi that isnt a cop show in disguise.
The other camp is the cable camp, where long serialized formats are highly popular, especially in drama. Space opera isn't in evidence but horror and fantasy based genres are very healthy. Look at the huge ratings for The Walking Dead and Game of Thrones. Audiences have no difficulty following complex, character-centric storylines on cable.
Star Trek can't survive on broadcast so it'll have to go on cable, or a streaming only service like Netflix, where the rules for original content are more similar to cable than broadcast. When Star Trek comes back to TV, it will have many of the characteristics expected of a cable drama - serialized, grownup, complex, violent.
I still think they'll draw the line at soft core porn, if only for old times' sake. But it will probably be noticeably sexier as well, hopefully grownup sexuality and not the sniggering juvenalia that we've been subject to far too often.