I don't know what historically confident knowledge you bring to that: I'll freely admit that mine is based on guesswork.
In athletics, any club, or school, or college, might have several people who would want to represent the team, and so the idea emerged, for the good of the social integrity of each club (Or school or college, I'll stop repeating that bit now), of having several runners represent it, in a relay. These are people who are together all year, who train and socialise in each other's company. It adds a cohesive effort to consolidate the group. It is a highly beneficial and deeply relevant discipline at that level.
As athletics expanded and inter-regional, or even international, meets started, the discipline, because it was on the schedule of club meets, was retained. But it ceased to have any meaningful cohesive element except in the sprint relays, where mutual understanding and adjustment to what each other are doing is relevant, it was just a throwback to the origins of competition.
The same is true of golf: I don't play, but both my brothers are keen. At any club, there is a strong social element, and a real cachet in representing the club in a match. A match against another club might consist of four or six independent matches being played, and because of the social element, there is more attention paid to the total result than the constituent games. And I know that the same is true of various racquet, and probably other, sports as well.
But divorced from that social origin, it is at best a weak imitation of those origins, and at worst a jingoistic supremecist exercise.
In the case of mixed TTT cycling relay, I would say neither of those extremes, just a meaningless aggregation, no more significant than some sort of totalling up of the men's and women's six nations rugby matches.