The Mission: Impossible films are a pretty unique case of a long-running film series

I'm not so sure.
I think there are critical screw-ups in the first three that are hard to reconcile.

The idea that Jim Phelps would betray everything he stood for doesn't sit well with me I'm afraid.
And if you imagine that he was part of the original stories in the late 60's by the time you get to this era he'd be at least 70 ?...nah.

The script for M:I 2 was a bit of a macho Man thing. One agent gone rogue because he wanted to make money from shares ?
Nah !
Shame too ! Dougray Scott is a fine actor pity his character was so one dimensional he didn't really have much to do !
M:I 3.
The whole Davian supposed arms dealer thing ? Not convincing enough for me.
Ghost protocol onwards have been much better and Benjamin Dunn as a character has been good. You can see the characters progression and his own unique skills
That's my view anyway.

I haven't seen any movie in that series completely, but concur with your statement on other series. And there is an exception to every rule, right?