The original intent of the federal "low speed electric bicycle" was that when compliant to the definition and requirements in CPSC 1512 the ebike was not a motorized vehicle and could be ridden anyplace a bike could be ridden. As you said that is the ultimate in simplicity and it made perfect sense. States have had "traffic / use" laws for bike for many decades and if they would not have drank the 3-class legislation koolaid that People for Bikes drafted and lobbied for. For some reason they just couldn't grasp one definition to be used a bike so they wanted to create a regulatory mess. The did a good job but that is not what a bike advocacy organization should have done.Florida does that one better. There are 3 classes of e-bikes there, but they follow one set of rules. You can ride them anywhere you can ride a bike. THAT'S the ultimate in simplicity.
Most will admit that the rules in many, or most, states are a collection of poorly thought out knee jerk reactions. The ONLY purpose they serve is so they had something in place. It's my belief that changes making much more sense will slowly roll out as the ebike crowd evolves. My thought anyway, FWIW.