But you can't safely guide the plug into the wall socket without looking at it. With European plugs[1], that's fine. The grounded version doesn't have that protection, but the female side has walls on the side and a protruding ground plug, so it's also safe to guide with your fingers: by the time the plug is sufficiently in to become live with power, the gap is smaller than the width of a toddler's finger.
That's exactly what happened in Europe. The old ones were as dangerous as the ones currently in use in the US. They managed to make the transition in a way that was backward compatible.
Here in the US we did change our plugs, by introducing polarized plugs. We don't have to be change-averse.
Sure, and the grounding pin was also added. To get around that, every hardware and department store sells those little defeat devices (that you're supposed to ground but I'd be surprised if anyone ever did that). That's an instance where the reaction to a change leaves you less safe, not more.
You could probably require the plug leads to have rubber coating on 80% of the plug material, and recess the actual contact points slightly farther back into the receptacle, which would emulate the British plug somewhat, but good luck getting anything like that past the lobbying of groups who often cut a tiny hole in one or both blades just to save fractions of a penny per plug
