I mostly agree, where it's reasonable. In places with a large presence of pedestrians, I don't exactly, except for on road design. The roads should come up and meet pedestrian level, not pedestrians going to street level, for example. This requires that cars go slower. It isn't an issue of pedestrian education though. Pedestrians shouldn't need education. The design should just work to protect them.
But yeah, usually cars "speeding" consistently is a sign speed limits need increased. Lower speed limits increase the difference in speeds of cars, some going the limit and some going the speed they're comfortable with (the speed fo traffic). This delta causes accidents, and the larger the delta the worse the accident. If people are always speeding, the limit needs to match them.