You're right, but you won't like the implication.
The solution is to not sell unlimited bandwidth. If AT&T sold data in packages by amounts, people would use that amount. If they went over, they'd pay more. They could raise their package to a higher allotment for a higher cost.
This would do two things:
1. AT&T would generate more revenue which would let them develop better cellular infrastructure to meet demand.
2. (And more importantly in the short term) It would discourage consumption. Lower consumption equals higher levels of service for those who choose to pay. If consumption is far below what the network can handle, a rate reduction will increase demand. If consumption is too high, a rate increase will reduce it (or supply extra funds for network improvement, if demand remains high).
Cellular never was unlimited at its beginning. We paid for blocks of minutes. As technology improved and supply of airtime increased, airtime prices went down. Unlimited airtime didn't appear for years after networks began.
Unlimited usage services are great if that usage doesn't harm other users. This is often true. Landline capacity is so high that local calls rarely interfered with others who wanted to make calls. There was no need to reduce call length. Long distance bandwidth, on the other hand, was relatively scarce (it wasn't uncommon to be unable to make long distance calls on Mother's Day or Christmas due to the trunks being full) so long distance rates discouraged people from calling unless they had the need. That also kept call length down which freed up the resource.
I'm not saying data needs to be expensive... it's just not practical for it to be unlimited, that's all; not, at least, until there's enough LTE and other technologies deployed so that everyone can use the technology and not be greatly affecting other users.
As a final point, some might argue that competitors are managing their bandwidth better. That might be true, and if so, people will be motivated to change providers. This will do as much to solve the problem as anything.
The cellular companies let us down in a way, letting us taste this cheap bandwidth and now we want to stream video and audio over it, download huge files, and access network content like we're at home no matter where we are. The airwaves can't handle it. It's time for a paradigm shift.
(I live in Canada, but we have similar problems. This isn't unique to AT&T.)