He was after-all, given the shield. Other options would be Spider-Man and Captain Marvel. But Spider-Man is still too young and inexperienced and Captain Marvel is presumably "too alien".
shareProbably Doctor Strange , there are not many options since they killed off too many major characters.
shareProbably not. He was more a follower than a leader.
shareFalcon was a sidekick, and I don't think anyone ever rises from sidekick to group leader, it's hard enough for them to be accepted as an equal, especially when they lack superpowers.
So who can lead? Rodgers was the semi-official leader because he was the strategist, the one who had the best understanding of how to use their powers in a combat situation, and that's what the Avengers need in a team leader, because they've got Fury to do the administrative stuff. So let's see, Spiderman is a kid, Captain Marvel is part-time, Thor is a dumbass, Falcon/Cap 2.0 and Vision are in flux, Rhodes is also dealing with the sidekick thing, Winter Soldier and Hawkeye are messes, Wanda just isn't a team player, etc.
So maybe Captain Sam becomes the leader in the future, but right now, the obvious candidates are Doctor Strange and Bruce Banner, and Banner literally can't think in combat situations. While if you give Strange five seconds, he can see how 14 million possible courses of actions will play out, so I think it's pretty clear who ought to take over.