Remember what I was talking about with the whole "throw" thing? With things like fighting games and shmups, you want that to be as short as possible, and every analog stick out there is going to have a longer movement radius than a D-pad.
Standard controllers aren't designed for fighting games or shmups, is the thing, and there's no reason they should be - after all, no one playing games in any other genre wants a short-throw stick, and that concept isn't really compatible with the concept of an analog stick anyway. Also, fightsticks exist for those people (and the stick on one of those has a shorter throw than any standard gamepad's analog sticks, and it's possible to mod many of them to make that even shorter).
Furthermore, games in these two genres almost never actually benefit from the main design feature of an analog stick, that being the analog movement. In fact, some home ports aren't designed to accept a slight movement on the analog stick, and force you to push the stick all the way to the edge to register input. Doing so is horribly inefficient, and I don't see any reason why I should try to use an analog stick in those cases when there's a perfectly good D-pad sitting there.
Which brings me to my next point: it's also much harder to do many standard inputs on an analog stick. Compare a double-tap forward or back on an analog stick to how effortless it is on a D-pad. Look at something like a quarter-circle or half-circle input, or a super jump (down-up); on an analog stick, you actually have to push the stick in those directions, whereas on a D-pad, you simply roll your thumb.
The only inputs I've ever had to do where I might prefer an analog stick to a D-pad are 360s and 720s, and that's more due to the fact that it'd be less painful to rotate the analog stick than to try to roll my thumb across the entire face of the D-pad in a single split-second movement. It doesn't make sense to switch to the analog stick in the middle of a heated battle for one input, though.