Shooting delay after sprinting and sprinting delay after shooting are present in both ETQW and Brink.
In RTCW & W:ET - don’t remember (but probably same as in Brink)
Quake Wars - delay is much smaller than in Dirty Bomb
Brink - delay is much smaller than in Quake Wars (practically immediate resuming).
In Brink it was needed because it was slow as hell already. Dirty Bomb is approximately as fast as ETQW (or maybe just a notch slower due to smaller maps). So my suggestion is, why not making the delay approximately same as in ETQW?