Sometimes I've gotten 200 applications for a job posting. Not for a long time, but in 2000-2001, after the Internet crash, it was ugly. You had no choice but to filter a lot. You did your best, knowing that you were missing some good candidates. But any little flag was enough to push you into the "no" or the "maybe" pile.
Even when I've gotten relatively few applicants, it's still time-consuming to bring people in. I wouldn't say that a bunch of short-term jobs would rule out anybody on its own, but I would still like to see something that shows you had an impact during your short time. And like others have said, there's a lot of value in seeing big projects through from start to finish, so there might be positions where I'd be like, sorry, I need to see that you've done that before I hire you for this job.
It's not the years, really, but what you've done in the amount of time you had. Like I said, the ones stated are mostly all good reasons for leaving a job. In an interview I woudld probably find them convincing. I also think it would be great to be able to say, for at least one job, "I stuck this one out and did everything I could, despite the odds stacked against it, because I really wanted to see something through."
To you question specifically, I think having at least one job with a longer tenure would be a big improvement to the first-impression reaction most hiring managers would have to the resume.