In meditation, should one pursue tranquility first, prior to looking for insight? On the one hand this question has been asked to death on the internet (and yuttadhammo's videos even try to handle it). On the other hand, I personally still don't feel I have a clear answer (and I don't think that's because I'm an idiot.)

From my overall reading, the commonest answer seems to be that while the primary aim in meditation is insight, it is not only useful, but advisable (and maybe even essential) that one first achieves some degree of tranquility or quiescence before moving on to insight. Specifically, it is advised that one attain at least access concentration, if not full-blown first jhana, before moving to insight work.

However, there appears to be an important exception to that rule, coming from (at least) the Mahasi tradition, wherein the idea of "bare insight" arises.

From the existence of those apparently different positions, I am confused in two ways.

First: if the bare insight thing is valid -- i.e. if it is possible to go straight to Vipassana without going via Samatha -- then why wouldn't everyone just do that? Insight is The Point, after all, (isn't it?) so why waste time with what seems to be mere training wheels?

Second: OK, suppose access concentration or first jhana is necessary, but is also sufficient a level of samadhi as preparation for vipassana. Then, again, why would anyone then continue on to "samatha" jhanas 2 through 4? My understanding is that while those jhanas may be cool and blissful, not only are they not The Point, they carry the danger of attachment. So why bother with them?

To pre-empt any "it doesn't matter" style answers, I really think it does. There are several apparently good teachers out there whose approach is, to paraphrase, "No, don't note yet. We're not doing that until we've got a bit of focus", while there are others who get you noting from day one. So overall it may not matter, but it matters to beginners (like me) as part of deciding on a teacher (and on how to meditate while I look for a teacher).
I will try to answer from my point of view as a Vajrayana practitioner. 

I've been taught that one needs to have a relatively stable mind in order to practice insight meditation. But this doesn't mean that one has to spend years in Samatha meditation before trying Vipassana.

In Mahayana and Vajrayana tradition too much tranquility and so-called 'inert peace' is considered as an obstacle on the way since it is not a full enlightenment and it can easily prevent a practitioner from pursuing next stages of realisation. To avoid that, practitioners can take a Bodhisattva Vow to remind them that they want to pursue happiness not only for themselves but mainly for all the sentient beings.

One Vajrayana Lama was asked whether we need to calm down and bring our energy down in order to practise insight meditation. He replied that we don't have to calm down at all, we just have to transform this energy into something useful. I found it very liberating, since, personally, I found it somewhat boring to sit in peace for hours. When I got introduced to insight meditations which involved visualising Buddha forms and receiving lights from them, I liked them straight away. Then I met some more experienced practitioners and indeed, they weren't particularly calm, rather lively, very joyful and stable at the same time. 

I would say that choosing the right practice and teacher is very individual. If you already think that attachment to blissful state might be an obstacle for you, maybe it is a sign that you are ready for insight meditation. It seems that you know enough theory so it is high time to put it into practice. Try not to overthink, just give it a try and when meeting a teacher or other practitioners, just ask yourself - do I want to become like them? Do I want to behave like them in 5 years time? If your answer is an honest one, soon you should find the right teacher.