What does the regional continuity model of modern homo sapiens origins not propose? premodern populations in europe, asia, and africa all evolved into modern homo sapiens. local populations would not have evolved totally independently from one another local populations would have evolved totally independently from one another?

The answer is - local populations would have evolved totally independently from one another.
There's no such proof that the local populations have evolved on their own and independently from the other populations. Constant contact, grouping, fighting, mixing, have all contributed that the changes appear on a much more massive scale, and that the independent local evolving was pretty much not existing.