Stanford doesn't even have those "registrar-imposed limits." Classes almost never fill up; they just get larger rooms or add TAs. Students don't usually register for classes until after the term has started!
I was an undergrad at a more traditional school where we registered for classes months in advance. I was amazed that the Stanford system was so informal, but in practice it worked just fine. It's wonderful to be able to audit a few classes before deciding on exactly what you're going to take; you may learn that you can't stand a professor, or love a surprising subject.
Wow, as an undergrad who has endured years of stressful schedule twiddling followed by a 2-week sprint to figure out how I'm going to replace all the crap courses I naively selected months ago, that sounds like paradise.
It's not exactly paradise. Because classes are only ten weeks total (slightly less in spring), you can't exactly spend the first week or two shopping around without doing non-trivial work for every single class you're shopping --- an approach which doesn't scale, to say the least. There's still a sprint the first few days. But still, it's nice.
I was an undergrad at a more traditional school where we registered for classes months in advance. I was amazed that the Stanford system was so informal, but in practice it worked just fine. It's wonderful to be able to audit a few classes before deciding on exactly what you're going to take; you may learn that you can't stand a professor, or love a surprising subject.