So I actually went and did some digging, because time blurs memory. Really, really hard to find good data, but what I can see from at least wrath onwards, bleeds between rend and deep wounds have constituted around 15-20% of arms’ total damage output.
I don’t know what you consider “whopping,” nor what you consider to be the cutoff for “acceptable” bleed damage, but bleeds have not been insignificant for warriors in a very long time, at least as far back as we’re still able to look.