Yes we do, but it'll never happen
Android dominates for the same reason as Windows did before it, because it had a bucketload of cash spent on channel partners, marketing and infrastructure.
The bit where people write the actual software is easy, and really has zero impact on adoption, no matter how good it is. The fact of it being free (in either sense) is even less relevant.
Ultimately people use software and services because other people use that same software and services. It's a momentum thing, and getting that momentum going needs serious muscle, far beyond the FSF's philosophical musings (all of which I totally agree with, but then I'm not 99% of consumers, who really only care about results, not how they get them).
The best chance we have of seeing something that is both free (as in freedom) and popular would be if you applied the same collaborative principle to funding as the actual free software development, so a truly free software mobile initiative could pay for all those things beyond mere software development that are absolutely necessary for market dominance.
In other words we need crowdfunding. Sadly even most of those go titsup, because nobody ever hears about them (as even crowdfunding needs marketing - catch 22).
Nope, there's just no way around it. You need big fat wads of greasy cash to do pretty much anything.