Despite all this, BTIG Research’s Walter Piecyk believes that supply and demand for Apple’s (AAPL) iPhone 5 are “almost in balance.”

In a note to clients issued Thursday Piecyk reports that ship times for the company’s new iPhone are down to a week at AT&T (T), Verizon (VZ) and Sprint (S) — a point underscored by AT&T CEO John Stephens at a Wells Fargo conference the same day:

“Supply was challenged in the third quarter,” Stephens said, “and quite frankly, the supply situation has improved, and we expect it to continue to improve, and we’re thrilled with that.”

So why does Apple still list all models as available to ship in 3-4 weeks?

Piecyk’s theory is that the company is pleased with its “new and popular strategy” of allowing customers to order an iPhone between 10 p.m. and 4 a.m. and pick it up at the store the next day. Besides reducing frustration, it brings customers into the Apple Stores, where the chances of them walking out with an accessory or two — or even another iOS device — increases significantly.

In any event, he thinks the company should have “no trouble” selling the 47.5 million iPhones he had forecast for this quarter, up 28% from last year’s blow-out Christmas.

“Apple’s best hope to re-ignite sales in the March quarter and extend the compressing product cycle appear to be with signing up China Mobile with a TDD-LTE version of the iPhone,” he writes.

But he adds that unless Apple is willing to cut its prices, the company is going to have trouble selling large numbers of iPhones in China and India, where most people carry pre-paid mobiles that they picked up for $100 or less.

UPDATE: Piper Jaffray’s Gene Munster reported Friday on his nightly survey of iPhone 5 availability at 100 Apple Stores (see chart below). “We believe,” he writes, “that based on trends in our checks for Sprint devices, it may only be another 2-3 weeks before consistent availability of AT&T and Verizon iPhone 5s.”