re:Wakanda 9:00 it is important to note this is only an option if you're deemed to represent a tribe or are a Royal Family member. In this way it's a release valve for the pressure of civil wars (if 2 Royals are prepared to fight to the death this usually results in them ripping the country apart, not just each other's chests) and part of the confederated state's basis, being an alliance of several tribes acting as one. This is why Killmonger had to prove Royal blood AND have the tacit approval of several disgruntled members of the hierarchy who he'd impressed by his fait accompli of killing a major enemy who'd eluded the ruler's forces after he promised to get them. To even get the duel was a calculated matter of politiking. In most cases Trial by Combat had rules over who got to initiate it or deem it legitimate, e.g. in Westeros nobles may invoke it for certain legal proceedings.
Realistically the least stable part of that plot, other than showing why that's not a great way to elect someone with vested interests in your state being stable/peaceful, is letting the first challenger go. In one sense it's more stable and prevents worse recriminations, but on the other hand if he's still rebellious he could raise an army or withhold assistance at a vital point. You've got to hedge your bet that the yielder's going to go home and lick their pride rather than foment rebellion, weighed against the possibility his successor would face pressure to draw blood as well. I presume this is why T'Challa's dad is so invested in intrigue and discovering who is loyal to his vision, going so far as to have his own brother killed rather than take him home and duel him-the appearance of a smooth, unchallenged reign with 1 personal tragedy. I wouldn't be surprised if he knocked off other challengers.