I agree, although "can't stick something out" is not always a negative connotation. The key is what the "something" is.
I've seen this pattern of resume for both high-performers and low-performers. Not everyone has the patience to wait for recognition and promotion that may be long overdue or just plain unavailable. By looking for those who have longer engagements, I think you'll find yourself safely in the middle of the pack.
(I'm not suggesting that you need to wait indefinitely for well-earned rewards, of course. It's just that I've seen a lot of "thinks they're higher-performing and delivering more value than they are" than the reverse.)
My longest engagement is about 2.5 years. The average length is probably around 20 months. I've left every position by my own choice and to the dismay of my employer. I'm not trying to boast, but it's clear from my evals, references, and repeat business I've received since being independent that I was and am highly valued. Each job change came for a different reason (family/personal, wanting more responsibility, etc.) and was not premeditated when I took the job. I can't say for certain of course, but I have no reason to believe any of those employers regret hiring me. You can be incredibly productive and a contributor over a period of 1.5 years. In our business that's a long time.
On the other side of the coin, I've worked with many mediocre performers who, due to lack of options, have recorded long stints at reputable companies. In my experience, for people to get let go, they need to be exceptionally bad. Average people stick around a long time. That's why I think using duration as a marker is double-sided. As you mentioned, promotions can be a good marker to offset this effect.
Previous job longevity is worth next to nothing without talking to the candidate in my opinion.
No problem at all.
I look askew at resumes where the longest stint is 18 months and the average is 12-15. That reads of someone who either can't stick something out, or someone that gets discovered as less-than-good over and over. Either way, I don't have a place for that.
A few 2+ year stints, a few promotions within a company, and still moving around a bit? That's normal. One bad fit job? No problem.
If you get another offer you want and you don't like the current role, switch. Life is too short. You might make it a point to stay at the next place longer than 7 months (ideally 24+).