Ray, I agree with your point about resolution. On the other hand, as I'm sure you'd agree, if you're shooting something like landscape, really good resolution can help the result. On the street, though, and in most other situations, resolution is vastly overrated -- because it's something Pop Photography can measure, I'd guess. At the risk of causing Dale to have a stroke I'd point out that resolution is lousy in some of HCB's best early photographs, but they're still exceptionally fine work.
If you are worried that the resolution of your camera is a bit inadequate for the print sizes you usually make or desire to make, you should either upgrade to a bigger format camera with a higher pixel count, or stitch images.
Alain Briot makes the excellent point that stitching allows for the possibility of capturing a scene that no single shot, however wide the lens, could capture. Cropping is always essential with such a process. (I wish I'd included that point earlier in my list of reasons for cropping).
However, there is another reason for stitching. When your camera's resolution is either inadequate for the size of print you'd like to make, or bordering on inadequacy, then stitching is the way to go. It's better to have more resolution than required than 'just' enough.
If you have to take multiple shots of a scene just to be sure you don't have to sacrifice resolution in post processing (as a result of cropping), you need to either stitch or upgrade your camera. Even those who have an 8mp Canon 20D which they think is perfectly adequate for the A3 size prints they always make, could benefit from the greatly enhanced creative cropping opportunities offered by the 21mp 5D2.
As regards HCB, he's a very unusual photographer. He used a range-finder Leica with a viewfinder that shows a wider view than the area covered by the film. There's a 35mm matte in the viewfinder, isn't there? I get the impression that HCB was like a tiger watching his prey and waiting for the best moment to pounce. The 35mm matte in his viewfinder was the critical area. In a scene with movement, he could see what was happening outside of the 35mm frame. As various elements moved in and out of the frame, he would be watching carefully. If he pressed the shutter just half a second too soon or too late, he would miss the composition, as a tiger would miss its prey without perfect timing.
Resolution is of secondary concern with HCB's art form.