The LS and RS are probably there only because for a lot of other games left and right stick are pretty crucial, and if you should just so happen to be playing them with the arcade stick (I don’t know why you would), you can toggle among LS DP and RS in order to navigate through the games. But if you’re playing Street Fighter, you should only be using DP, not because “everyone does it,” but because LS and RS are supposed to replicate analog sticks, which themeslves are supposed to replicate certain movements (which is why they’re good for flying games, fps–games that require some type of camera/FOV movement). They’re not meant to be precise direction inputs, whereas you need precise direction inputs for serious fightings games like SF. Try this in training mode: put it on LS and move the stick forward or back, and then back to the neutral position, you see that the character still moves for like a second. With a game were spacing is crucial like in SF, that isn’t gonna fly.
I suppose that’s why people most people don’t like along sticks even on pads, although I find the sticks on pads to be good enough for the job that using the dpad or the left stick would be a matter of preference.