The first mate has 2 jobs in One Piece:
1. Represent the crew if the captain is gone, especially when confronted by an enemy faction.
In order to fill that role you only need strength and reputation, nothing else matters. Zoro was qualified for it the most throughout the series, other crews and organisations naturally consider him the second in command due to his name and fame (Saobody Arc). If Zoro isn't around, that role is filled by those next in line when it comes to notoriety (see Sanji during Zou - only he had the necessary reputation to negotiate with Bege eye to eye)
2. Ensure order. Even more so if the captain is a meathead.
Obviously this is Nami's role ever since, not only when it comes to money or navigation. Her word easily has the most weight when strength and reputation isn't a factor.
Characters like Killer or Marco fill both aspects, while Oda was clever enough to split the "first mate responsibilities" between Zoro and Nami. That way he avoids establishing a hierarchy within the crew, something that absolutely has to be avoided when you want to tell a story about a group of friends having an adventure.
That said, this is also the reason why Zoro will fight someone notorious very soon. I don't want to turn this into a Wano fight thread, but he will, 100% sure, fight an enemy with an insane bounty so his own also raises dramatically. This is Zoro's character, his job, his dream. It's a pillar of his character.