Meh a new "TOS" series would be a bad idea to me. For any number of reasons. One, they wouldn't be able to afford the current cast as they're already 7 figures plus established stars now. So you'd have to recast some or all of them, which would alienate the fanbase more.
The biggest reason is, a reboot is just the ultimate lack of creativity. You take existing characters, in an existing setting, change a few details, and boom.. you have a "new" story. I'd rather see something genuinely new and original than a rehash of something that's already been done. Even the reboot, after lamely establishing the "alternate universe" in an attempt to appease the older fans, just went to that formula with the recent movie. Oh it's Khan. Wait we're probably gonna bring him back in the sequel too. Can't have Kirk and Spock facing a new villain or anything. Guess we can have Koloth and Harry Mudd in the next one. A series would invariably bring in every past villain from TOS at some point or another... the movie franchise as long as it goes is already trying to do this.
It doesn't even have to be a random group of people we don't know. Heck bring in John Cho as Captain of an Excelsior series in the rebootverse, that'd leave a lot of room for original storytelling that hasn't been done before. Or if we want to get back to the Prime universe, do a Titan series and recast Riker/Troi. You could even bring in Patrick Stewart as a guest star, "Admiral/Ambassador Picard" now and again since the man doesn't age.
You can make a connection to the past without blatantly ripping it off, mixing it up and trying to sell it as a new product. It just requires a slight amount of creativity. Even then you don't -have- to... TNG and DS9 did just fine with a new crew. a Series set in the early 25th century with Admiral Riker passing the baton might be interesting too.
But don't worry BillJ, your line of thought will probably prevail. Hollywood would rather redo something that's been done, than do something new after all. There's no risk in that.