The government also invented the freeway system and the internet, and those didn't turn out too bad.
This conversation is a moot point in Japan and many other countries, because here (in Japan) we have competition rather than the rampant collusion among the American carriers. There are still unlimited data plans available on every carrier, and they're getting cheaper due to portable wi-fi hotspots in 3G, LTE and Wimax flavors.
As for capacity, it's not about airwaves, it's about server collisions. As you said, it's going all data, and American phone companies are loathe to cooperate in sharing the actual wired data networks, let alone upgrading their own. They've always been very good on making excuses as to why they can't build out their infrastructure while the rest of the world moves forward. They rely on natural American insularity to protect them from comparisons with successful systems abroad (and no, geography doesn't play as big a role as they'd like you to believe).
The government has attempted to play fair and leave this in the hands of the carriers since the 90s, even doling out billions in grants to help these companies in building out aforementioned infrastructure, but the companies have merely pocketed the money while thinking up new and interesting ways to screw their customers over.