Warband's Floris mod had a good tournament system (not sure what original mod it was based on, but credit to that). You get points for each individual KO plus points if your team wins, and there is no elimination, just six fixed rounds. They also had extra awards for fiercest competitor, strongest cut, etc., though not sure how that was implemented or how much sense it made in the end.
Yes single elimination is easier to illustrate and easy to understand, but awarding points in each round based on last-man-standing as opposed to say number of KOs per team is less so (and there's even a score counter already implemented!).
The arena overhaul in Floris was silly imo: messy beaten-up terrain with obstacles that would be downright dangerous to run a horse through, random trees and shrubs that would obstruct spectators' views, all making zero logistical sense (similar to the giant immovable rocks in Vlandia tourneys in BL). Historically in arena games, creative obstacles were definitely a thing, but so was practicality. You had to be able to move obstacles into and out of the stadium, you had to be able to see the competitors, and you had to not cripple the horses and gladiators just by moving through them.
To the latter point in general, arena games really should not look so obviously deadly to horses and competitors. This would require a lot of redesign and a lot of new development, which is also why we won't be seeing jousting or even archery competition any time soon. We can still ask.