I think it's both working harder and born with it since Zoro have bloodline too.
What power has Zoro gained from his bloodline so far?
All his swords he gained by training and proving himself to the people who had them prior
Wado by becoming Kuina's rival and asking to inherit her will
Sandai and Yubashiri for taking on the curse and surviving, while also making the shop keeper impressed
Shusui for defeating Ryuma in a battle and showing his strength while nerfed, only having 2 swords
Enma by defeating Kamazou and saving Hiyori, who was the owner of the sword and decided to gift him after showing how strong he was
CoC is because he is a shimotsuki? I wonder if Oda is gonna confirm that Ushimaru and Ryuma were also CoC users, i doubt it
Asura is from the Shimotsuki? maybe this one is, so far we don't know