Not in my experience. The road widths were set hundreds of years ago and the buildings have not changed. Walking around European and UK towns I find myself much closer to cars than walking around in the US. This is a factor in keeping car speed low, which likely affects how often and severe pedestrian collisions are.
I do agree that European roads are safer, but not because they have made large segregated sidewalks (which is what I disagree with as reality and the root cause).