PgSQL is great for a lot of things, but I would argue that if you're using it you're betting on your overall product/service having some other killer advantage than data processing. The competent wing of the NoSQL crowd are using it in strange ways that enable new classes of product and service that cannot be achieved with PgSQL.
Though your last line makes me curious. What is an example of one of these new classes of product and service that can't be achieved with PgSQL?
My broader point is that if your project fits into pgSQL then you need another unique selling point and the data functions are just an implementation detail of some other aspect of your offering, whereas for many of the people not using that kind of thing their analytics and data systems are their selling point. (That's a backhanded compliment to pgSQL, in that it's easy enough to get right on small systems that any competent developer should be able to manage it, thus reducing the market value though). There is, of course, the blurred line of crazy MySQL deployments, many of which are barely relational.
That doesn't make sense to me because it only really applies when there is a high likelihood of competitors using one product but not the other. Although postgres is doing great, in most markets it's still far more likely that your competitors are using oracle or sql server. So any advantage postgres has -- and I believe there are many -- offers a potential competitive advantage.
For instance, you could argue that data systems are a critical selling point of Heroku, and they use postgres.
I think your point ultimately boils down to: "postgres is not quite at the forefront of certain analytic use cases", which I agree with. It is at the forefront of many other use cases though.
pgSQL does what it does easily enough that it reduces the barriers to entry to such a level for traditional RDBMS workloads (which there are plenty of) that such workloads are simply not economically worth pursuing (especially for startups) except as small components in larger systems where the value add is elsewhere. The "other" world of big data/time series/graphs/nosql is hard to get right, and so is worth more, as if you crack it someone else copying you is decidedly non-trivial, meaning that it alone can form the core of a successful business.
This is a bit like what the web people are trying to do in mobile, where if HTML5 was magically the best cross platform mobile deployment option when we wake up tomorrow the value of mobile developers will collapse, and the web people will then cease to be remotely excited about mobile.
An interesting point. More broadly: if what you're working on is not hard (and awkward), then others can copy your idea easily. Technology like postgres makes a new class of problems easy, and thus you need to find new problems to solve if you want a sustainable business.