I think relays have no real place in cycling: no tradition, and not much to add as a novelty.
Relays in general are a poor form of team event: there is a real skill in handovers at speed in 4x100m sprinting, but beyond that it is simply a matter of aggregation of individual talent, not teamwork.
Where sport is primarily social, at amateur club level, I can see relays, and adding the results of individual matches, as having a place, but where we are looking at serious elite competition, it simply undervalues the ability of the best and promotes the importance of whoever is the team/nation's 4th(or 6th.or whatever) best athlete (or 2nd best sex).
And in terms of mixed events, racquet sports work, mixed foursomes in golf is tenable, and there are sports designed for the purpose like korfball (although I don't thing I have ever seen that played) . Some sports could be adapted for mixed teams perhaps: where a player is restricted to part of the playing area like netball or volleyball it may be possible to tweak rules such that men are up against men and women against women.
Other sports are suited to unisex competition: darts, snooker, equestrianism, motor sport, there may be others.
But I don't understand the idea, if that is what is at play, that women's sport is best enhanced by being in pseudo-competition with men when that obviously cannot be competitive.