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.