I think a 2 year PhD is very atypical in my field (CS). In my experience I learned a different lesson than you when it comes to 3 and 4. I found that more important than anything, picking an advisor is the way to choose your PhD. They have such an outsized role over your experience, much more than the University, Department, or even the problem IMO.

To give some context as to my experience:

- PhDs are funded. You get a stipend and tuition is paid for. This funding is either through a research assistantship (RA), or a teaching assistantship (TA). Either way you are expected to devote 20 hours a week to this task, and the rest would be devoted to your coursework. Typically you take 9 credits per semester for about 4 years, and then after you enter candidacy (you're not really considered a PhD candidate until you pass qualifiers, before then you're a mere PhD "student") you reduce that to a 1 credit "dissertation maintenance" per semester.

- Grant money is the lifeblood of a PhD granting research-focused department. Here's how the economy of a typical CS department works:

-- Newly hired faculty are given a "startup grant" that they use to bootstrap a lab. Their motivation is they want to get tenure in 6-8 years. To do that, they will need to justify to the Dean that they are capable of generating sufficient grant revenue.

-- Grant agencies award grants largely based on published research papers. Therefore the primary directive of a new academic is to publish research, and use that to obtain grants. Hence the phrase "Publish or perish"; if a researcher fails to get enough grants when the tenure clock is up, they will usually be put out to pasture; failing to get tenure is the death knell for a young academic's career.

-- So they hire a couple PhD students as RAs and they work on producing research papers for conferences. The new academic uses the published research in grant applications (the first target is usually the CAREER award). Soon enough grant this grant money is flowing to the researcher and they use it to pay for all sorts of things. Chiefly though, it is used to pay for the stipends and tuition of graduate RAs.

- As an RA, you will be expected to spend 20 hours per week on grant funded research. This means you don't have room to explore your own research topics! All of the grant money is allocated for the funded grant research, not your own whims. The best you can do is carve out some interesting angle on the research that you can call your own.

- By the time you get to maintaining your candidacy, you're already knee deep in publications on the funded research project. The path of least resistance at this point is to bundle them up into a dissertation and defend it.

- If you have your own research agenda, now is the time to execute it as a faculty member at another University. One of their primary concerns during hiring will be: "How is your research agenda different from your advisors?" You will perhaps not be surprised to find that many candidates fresh out of a PhD program will not have their own original thoughts yet. This is why many departments prefer that a new PhD actually take some time doing a postdoc where they can gain some independence from their mentor.

Anyway, what I would say is that instead of picking a problem or a university or a department, pick a person you want to work with for the next 5-8+ years. Like I said, 2 years is very atypical. In my department, we have built in buffers that would make the minimum I think 3 years with a Master's, and even then I think the typical time would be 4 years.