How do you arrive at 100km/h if you're averaging over distance?

I don't doubt you're right, but I don't see it. My calculation is as follows: suppose the distance between both cities is 120km. The trip A -> B thus takes exactly one hour. The trip B -> A takes 1.5 hours (120km / 80km/h) = 1.5h. The total trip therefore takes 2.5h, the total distance is 240km, which averages at 96km/h (240/(1 + 1.5)).

A simple (V1 + V2)/2 is surely possible, but I don't see the value of that average, I can't think of a situation where it would be useful.

I think you are thinking about a case where someone goes 120km/h for 1 hour and then 80km/h for 1 hour instead of going over a fixed distance at 120km/h and then going over the same distance at 80km/h.