Lack of POV for Warband hurt viewership along with the lack of interesting elements.
Most esports have flashy or key moments with special abilities and a rise and fall to action that casters can form storylines around for individual rounds and the entire match. On that note, the way most Warband matches ended was anticlimactic, except for the rare instances that went to tiebreaker.
CSGO or RocketLeague are the most similar esports to M&B, but even CSGO has extra concepts outside of "shoot gun to kill" such as tactical smokes/nades and gear progression. CSGO and RocketLeague are based on incredibly high skill cielings. Bannerlord has neither.
Skirmish is a disaster of a competitive mode that I've hated since day one. Teams reach the tipping point of round wins too quickly, but then the rounds dredge on for another 3-4 minutes until the eventual snowball is resolved. BETWEEN rounds is even worse, with 390 gold reaching up to as much as +50% value. (Ex: 300g = Knight+Peasant, 390g = Knight+Vanguard.) Respawns make the game problematic to spectate. Melee TTK is still laughably slow against shields, and archery isn't very impressive because everything is slowed down so much.
Captain is fun to play between coordinated teams -- in fact, that's basically the only time that it's fun to play -- but would be incredibly boring to spectate and currently has significant AI and balancing problems. It has a future of being a fun competitive mode, but won't attract much attention outside of those who enjoy playing it.