This is a big reason why I'm wary of making her the team's new leader. While it's true that she'll have appeared in the same amount of movies as Captain America, I don't think it's organic to have Captain Marvel swoop in after years of being a lone agent to suddenly assume a leadership position. Captain America at the very least had leadership experience, but Captain Marvel's character is seemingly built upon her independence (forgive me if this is incorrect, as I actually haven't seen Captain Marvel yet). It doesn't seem like she'd take to leadership right away--she needs more time to grow and develop in order to become a major character.
I'm in agreement with @Sabretooth's choices, but I would personally opt for Thor (if he survives Endgame) over Black Widow. He beats Black Widow for me because he, like Captain America, has also been placed in direct leadership roles as the Prince/King of Asgard, whereas Black Widow has always been more of a lone operative without subordinates on her missions. Thor also has access to the Bifrost, meaning he can assume an authoritative presence and respond to threats in various locations across the galaxy, which is good for a leader. Additionally, he has endured a number of testing experiences that make him a prudent warrior (although Black Widow has as well). Another thing is that Widow strikes me as similar to Captain Marvel, in that she prefers to operate independently, and her personality makes me think that she'd be likely to pass on leadership to someone she was willing to follow.
It's not that I dislike Captain Marvel (I haven't seen her in action yet, so I can't make a real judgment), so my objection to her being leader is solely based upon how quickly she seems to have been forced into the mix, assuming a priority position above characters whom I think are more deserving of a leadership role because of their developed presence in the MCU.