On topic, although RTCW / ET were my first games I’ve actually played more DOD:S than any other game (and in DOD:S you can’t shoot while sprinting), and in the 6 years I played DOD:S despite coming to it straight from ET (and RTCW before that) I never once thought “damn, wish I could shoot while I’m pressing my sprint button”.
As someone’s mentioned already in this thread it’s not about shooting while sprinting, it’s about shooting while moving at your default speed. As long as you can do that (and what FPS wouldn’t work that way) I don’t see why you need to also be able to shoot while artificially traveling faster (or slower) than default speed. For me it’s a trade off, when you sprint what you gain in speed you lose in not being able to shoot while doing it.
If you can shoot while sprinting, and assuming there’s no stamina bar, why would you ever not sprint? And if you’re always sprinting why not make it the default speed? If you’re going to have different speeds there should be a difference in what happens when traveling at those speeds (beyond the obvious) IMO. And personally I’d rather lose the ability to shoot when sprinting than add spread as a counter because spread = luck and I don’t think luck should have any place in a shooter.