Interesting. What would this be able to do ? Current wireless speeds, even with state of the art technology, is going to be something like 10Gbit. That'll have to be shared by an entire city at least (correction: about 2 satellites per state on average. Less for New York), and of course there won't be any CDNs or HTTP caches "upstairs" so to speak. So 1 bit in = 1 bit back out.
Even at 4425 satellites that means, let's see. The earth is 500 million km2, and they don't need the same density everywhere, so some optimizations may be possible, so let's say 5000 satellites. That means 100,000 km2 per satellite. That means one satellite per decent sized country, only about 100 for the entire US. This is not geostationary orbit, so they'll have to aim for evenly spaced satellites.
Let's say they fix their satellites and do 10x what is currently possible, so that means 100Gbit/satellite. Current internet traffic into and out of the Netherlands is 50 times that (granted, more and denser cities than portugal, but the Netherlands would have to share one SpaceX satellite with Belgium and parts of the UK).
They would only be able to provide about 1/10,000,000th of a Satellite to a cellphone in the US, and if they have 100 Gbit/satellite, that's not even 1kbit on average. Even 10x or 100x that capacity wouldn't change much. Doubling or tripling the number of satellites won't fix this, we'd need between hundreds of thousands and to millions of satellites.
This will either need to be rather expensive (certainly as much as your cellphone, probably more, as this seems to indicate the system can only support 100x less users than the mobile network in the US, and even less in smaller dense countries or cities like the Netherlands or New York). Even at state of the art technologies, bandwidth limits are going to be tight. Like any satellite service, I can't see this work at city densities, or for mobiles.