I don't ever recall seeing a 2 handed bronze sword, and if the steel is worse than bronze, why didn't they go back to that? Which kind of suggests that it isn't.
I'm assuming low quality steel is overly soft rather than overly brittle. If it were overly soft wouldn't that favour shorter blades? You'd either get flex, or as you mentioned, added weight, which seems a bad trade off compared to a shorter sword and shield?
I got the impression 2 handed swords/no shield was an honour thing, rather than a tactically advantageous thing, I'm in no way an expert on such things though.