Just a wild guess here, you only ever drive right?
Sidewalks work in cities where traffic (vehicle and pedestrian) is always high and areas where you have massive amounts of space for them (mostly places built up after WW2). For areas where sidewalks are not practical a wide shoulder is almost as good IMO. Obviously it depends on the nature of the road as well.
Personally I bike and walk exclusively (do not own a car) and would much prefer separated cycling/walking paths. I get that there is a cost associated with this, but I think the cost is comparatively low to that of even marginal improvements to highway infrastructure.