In hundreds, nay - thousands of dungeon runs over my tanking "career" I have never seen anybody stop casting at the currently engaged mobs simply to pull more.
This sounds a bit made up honestly.
Once you have threat, you can - and should - be moving towards the next pack. Stop at the boss and cleave everything down. The only way people are moving ahead of you is if you're standing still waiting for a pack to die...
Or maybe if the DPS is abysmal you'd stand still waiting for damage, in which case they usually don't pull more mobs anyway in my experience.
You can do most dungeons in 3-5 pulls right now.