@Harp I’ll answer two parts to your question: cultural and practical reasons why fixies are popular.
Fixies have been quite popular amongst the courier community for a while (I’ll talk about that in a second). When I lived in SF from 2003–2006, fixies had started to become adopted by the hipster community—possibly for the same reason that I personally got a fixie: I dated a former courier. By 2006, though, they were firmly entrenched in hipster culture, and you started to see pre-made fixies being sold (instead of building them from old track bikes or converting old road bikes). Part of the cultural adoption also lead to hipsters getting fixies purely for aesthetic reasons (which had always been a part of the courier culture, but not nearly to extent that you see now). All of this also coincided, in San Francisco, with the adoption and proliferation of messenger bags and the rise of popularity of chrome as a bag (when I bought mine in early ‘03, no one outsid eof the courier community had really even heard of chrome bags, now they’re nearly ubiquitous in SF).
Now, practically, they’re actually only suited for urban riding, for precisely the reasons you pointed out (since coasting and going down hills are the worst parts of having a fixed gear). The lighter weight helps, but mostly the fact that you have very little chain slack means that it takes very little time to adjust your speed—meaning that your reaction time is much faster on a fixed gear bike. It makes timing traffic in an urban environment much easier since you have much more nuance in slowing down and speeding up—which is very useful for a courier. It’s not so much the fact that there is one gear, but the fact that you can intuitively and quickly match speed to the traffic moving around you that makes them appealing. Also, the way they’re geared means you have great power starting from a stop, it means you can trackstand much easier, etc.
Personally, I’ve always had brakes on mine, but there is a macho urban-chic aesthetic reason for having a stripped-down bike. So, yes, they’re popular for precisely the reasons you mentioned—all of them.