will AT&T get better once there is a verizon iPhone?
Funny you should ask that question that way.
I've watched AT&T over the last 10 years since jumping back and forth between Verizon and them multiple times. In my experience, they have never seen this kind of growth and profitability since their exclusive release of the iPhone. Unfortunately, they literally sat on the piles of cash they raked in, and padded their pockets until last year when their network and disgruntled customers couldn't take it anymore. Their greed was and continues to be evident - charging an additional $10 for 3G data over 2G? Charging $20 a month just to flip a switch for tethering? Mandatory data plans and killing unlimited? Garbage PR and campaigns such as "Seth the Blogger Guy" and "Rethink Possible" instead of actually fixing the problems?
Add to the fact that this "exclusive US carrier" typically carried less than 5% of stock than their corresponding Apple stores shows that they didn't want to unnecessarily give commission to their own employees when they could rather let Apple do all the white-glove sales and activations for them for free.
Knowing that their exclusivity is finite, they - in typical Wall Street mentality - decided on the cash grab approach instead. So, when the exclusivity ends, profits drop, operations scale back, and workforce reduction ensues, the suits at the top will already have their golden parachutes padded and ready for use.
I sat next to a Sprint user with his HTC EVO 4G on the train yesterday from NYC to Central NJ. And while I don't care much for Android or Sprint, I was watching him thumb through fresh web pages like a book. When I wasn't going through dead zones that repeatedly gave AT&T on their "Mark the Spot" app, I stared at a waiting icon while my iPhone 4 eventually figured out it couldn't pull any data from AT&T's overburdened towers. As I said before, it's like driving a Ferrari down a highway with a kid in the passenger seat, yanking on the parking brake every other mile.
Going back to your original question, it's my opinion that AT&T won't "get better," but it might "suck less" in your personal experience.