I believe it's the opposite. We're meant to do the first titration quickly, hence its name "rough titration". We never take into account the results obtained from the first titration, as we only use it to give an approximate result. Say you just let the biurette run, and it changes colour at around 25 mL, but your reaction time isn't fast enough, because you were just letting it run. In the second/third/fourth/Nth titration, you can now let the biurette run for the first 20 mL, THEN let it drop very slowly, so that you don't have to waste time dripping it for the whole titration.