I fail to see how Zoro having important parentage somehow de-legitimizes his feats or progress. If that is the case, then what does that make of Luffy? Do all of his accomplishments and hard work not matter because he is the grandson of the hero of the marines, and the son of the most wanted man?
If Zoro's dad is say Ushimaru, or Ryuma is his ancestor, he's still Roronoa Zoro. He wasn't shielded or buffed from his connection to them. No one as far as we know is even aware of Zoro's connection to them if it were there. Zoro himself isn't the type to dwell on his past, nor consider it a benefit on his quest.
Now, if Zoro is indeed just a rando from East Blue, great. But it's not like the alternative ruins his character or story.