Warning: massive spoilers ahead
Captain America doesn't just lead, he is a leader. People defer to him by default, often without really thinking about it too much.
For a new King, who's already struggling with stepping out of his father's shadow and away from his legacy, that's a real problem.
T'Challa is already having image problems, he put a huge amount of his reputation on the line when he gave his word to bring back Klaue. When Klaue was freed and subsequently delivered as a warm corpse by Eric Killmonger, T'Challa's credibility took a huge hit.
Relying on Captain America to solve his immediate problem wouldn't fix the underlying threats to his reign.
On a meta level, the "Black Panther" movie wouldn't have worked if there was any credible "White Savior". Rodgers is a great person, but there's no getting around the fact that his background makes him a really bad fit for this movie.
Now for the elephant in the room: Everret Ross.
Ross has a really important role to play in the meta narrative of "Black Panther". He's assertive in his sphere, but as soon as they get to Wakanda he does exactly what is needed:
- Ross offers only that information for which he's legitimately a domain expert (what the CIA taught Killmonger) or about which he's asked.
- He listens, pays attention, and does his best to assimilate rather than assume they'll accommodate him.
- Most importantly: he does what he's asked, and doesn't try to run the show.
There are exactly two points were he deviates from this pattern.
The first is when he asserts that he's with them to the end, which is no more or less than what the others are doing. He also justifies his assertion when questioned, and then shut up, making it clear that the final call was theirs.
The second was making the judgment call that he had enough of a chance to complete the mission he was given that it was worth risking his life to keep going. As a pilot of acknowledged skill, gambling only his own life, that was a call he was entitled to make.
Thus Ross did not present the narrative issues that Captain America would have, and provides a decent template for how white people can be helpful without causing more problems than we fix.