Why didn't Black Panther ask Captain America or the other Avengers for help (perhaps from members that are hiding in Wakanda due to the Sokovia Accords disagreement) when trying to reclaim the throne in Wakanda?
We can see that they were clearly outnumbered in the Wakandan civil war. He could have surely used the help of Cap and his team of the Avengers.
As the tie-in comic Avengers Infinity War Prelude shows, Captain America and his team of Avengers are not hiding in Wakanda. They are off trying to recover the remaining Chitauri weapons and technology and keep them out of the hands of terrorists (and former disaster clean up crews).
Bucky, however, was in Wakanda. In an interview with Collider, director Ryan Coogler explained why he was not asked.
But Bucky would have horrible PTSD, he would need spiritual guidance. The last thing he would need to do is jump into that Civil War, and so that was kind of the thought process there. And it could be potentially problematic if it’s a bunch of Africans fighting and you bring in a White dude, he comes in shootin’ people (laughs). We were aware of that. Bucky’s not trained to neutralize people peacefully, he’s an assassin. We were like, ‘I don’t know if we can do that…’” (laughs)
The writers could certainly rationalize the presence or absence of Captain America and the other fugitives during the Wakandan civil war, but from a storytelling point of view Captain America's involvement would undermine the themes of Black Panther.
Wakanda is presented as a African nation that tapped the mysterious powers of vibranium to advance its technology not only beyond that of its neighbors, but beyond that of the Western world. Camouflaging itself as a nation of herders with no resources of interest, Wakanda avoided detection by and conflict with the European empires that carved up Africa during the 19th and 20th centuries.
Aside from the use of relatively advanced weapons, this conquest of Africa often saw the Europeans gaining allies and subverting regions by supporting the claims of some tribes over others. Later, during the Cold War, both the United States and the Soviet Union would support revolutions in key African nations to put into power dictators that were friendly to their interests.
In Black Panther, T'Challa is the latest black African leader in a line of leaders who have been independent from outside forces for centuries. He is surrounded by fellow black Africans who have embraced his leadership and his goals for the nation of Wakanda. For the deposed T'Challa to rely on the (very white) Captain America and/or the other fugitive Avengers to overthrow Killmonger would embrace the legacy of colonialism and undercut the idea of Wakanda being a nation of Africans, for Africans.
(The only way to write around this would be to have Captain America participate in the battle in a way that doesn't meaningfully affect its outcome, which is exactly what happens with the only white character involved, CIA agent Everett K. Ross. While T'Challa and his allies fight Killmonger and his allies, Ross winds up remotely piloting a drone on a side mission.)
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:
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.
Taking a different tack here, we see in Thor: Ragnarok that the Avengers generally don't get involved in other Avengers' personal issues (for a given definition of 'personal'). Bruce, for example, tries to wave off Thor by insisting he doesn't want to get involved in 'family issues'.
I don’t want to fight your sister. That’s a family issue. - Bruce Banner
In the case of Black Panther, the issue at hand is similarly localised - it's T'challa's kingdom, it's T'challa's family power struggle, it's not something the Avengers should or would really want to get involved in. Everett Ross did get involved, but even then he's CIA, not SHIELD - and then only as himself, drawn in as a side effect of T'Challa's personal decision to save his life, not as a representative of the CIA.
If Killmonger had succeeded in shipping out Wakandan weapons and starting a global war, then the Avengers might have gotten involved, but since he didn't, we wouldn't know.
