The edge cases seem to be mostly around city driving, rural back roads, and bad weather.
And yet all the automated driving driver fatalities have been on the highway, with the Mountain View crash in particular having been caused by weathered / confusing road markings.
I wouldn't consider that solved at all.
But to the larger point, self driving lanes would only be a first step. Eventually it would develop into a standard set of markings and signage for automated driving friendly roads so that you could safely have self driving cars in things like snow storms.
There's no need to limit it to highways only, although there I think there is some benefit in the near term to segregating automated driving cars from human driving ones.
Practically all the edge cases, all the difficult situations and complex maneuvers are done in cities. Outside cities driving is very simple and safe (if you stick to the limits).