I would love to see it. While I like the MI Movies they just are not the same due to the focus on one character vs the ensemble dynamic.
They've gotten steadily more ensemble-y over the past few movies, with several recurring characters being gradually accreted onto the series.
Rogue Nation's team consisted entirely of returning characters from previous movies, except for Rebecca Ferguson's character who wasn't technically part of the team. In fact, it got a bit awkward, since Ving Rhames' and Simon Pegg's characters were both "the tech guy" and so they kind of had to be split up throughout the movie so they didn't overlap. The upcoming sixth film is bringing back all of
Rogue Nation's protagonists except Jeremy Renner (who would've been back if not for his
Avengers duties), and is also bringing back Michelle Monaghan from M:I:III -- making it the first film in the series to bring back a previous film's female lead (two, in fact) for a speaking role.
Realistically though, if you did do another MI TV series while I liked the second series that worked as a continuation and sequel (like TNG), I think at this point you'd be best just create a new team with a new leader and have no in-universe ties to the old series other then the normal it is an MI team and this flash drive will self descrupt in x seconds kinda things but don't tie any characters to any earlier characters and just start fresh..
I'd like to see something that goes in the opposite direction from the big, flashy government-backed spy stuff of the movies and develops what I believe the original concept of the series was: an unofficial, deniable black-ops team, basically a garage-band spy operation in which a retired agent, unofficially working for his former agency, recruits various civilian specialists to go on missions so sensitive and dangerous that they can only be done on a volunteer basis, with the knowledge that the government will disavow them as rogue operators if they're caught. Also, one other thing the movies haven't really captured is that M:I wasn't a spy show so much as a heist/con game show. It was inspired by the heist sequence in
Topkapi, but presumably the reason it was built around spies is because the network censors wouldn't allow criminals to be portrayed as heroes, so the con games and robberies had to be committed against enemies of the US and the world.
The thing is, I'm not sure M:I's premise really works in the modern world. The ubiquity of facial-recognition cameras would make it pretty hard for anyone to successfully go undercover, or for an agent's true identity to be unknown to foreign agencies. In real life, most spies just work out of embassies and recruit local people to gather information for them. Of course, that does kind of fit with the core idea I described, recruiting civilians as amateur agents. Still, having the same people play different undercover roles every week wouldn't be sustainable for long. Unless they all wore M:I's impossibly perfect masks all the time, but then the lead actors wouldn't get enough face time on camera.
While I love serialized storytelling there is something to be said about a pure anthology series like TZ or Outer Limits. One thing really cool about them is that you really have no idea what is going to happen. You cannot assume that a main character is going to survive or not. I remember at least one outer limits episode that ended with the world being destroyed. A pure anthology is the perfect example of nobody and nothing is safe and anything can happen.
The weirdest thing to me about Showtime's
Outer Limits revival is that it had clip shows. Like so many shows from the era, it was required to do one clip show per season to save money. So they had to take installments of an anthology, stories meant to stand alone, and somehow knit them together into a shared reality. It was bizarre.
The only way I can accept the Mission Impossible movies are as a reboot or a alternate timeline or something. In fact, I was so disgusted with what they did to the Jim Phelps character that I haven't even seen any of the movies since the first one!
I think of the first two films as failed pilots for a series that didn't really kick in until the third film. As
MakeshiftPython said, they don't even feel like a series, just a couple of standalone films with a common title and lead character name. The first film was a standard Brian DePalma paranoid thriller, the second film was a standard John Woo action cartoon, and the third was basically J.J. Abrams doing
Alias with a feature budget. But once Abrams and Bad Robot took over, the series started to feel like a series. The past three films have had a consistency and unity to them that the first two films manifestly lacked.
So I recommend starting with M:I:III and moving on to
Ghost Protocol and
Rogue Nation. You don't need to know anything from the second film, or even the first, to follow the Bad Robot-era films. RN does make a passing allusion to the events of the first M:I, but that's the only time I know of that anything from the first two films is referenced in the later ones.