"Why are nested functions better for sharing variables between workspaces than global variables?"
Nested functions provide much better control over where those variables can be accessed from. This is huge benefit from a code design perspective, because it makes code easier to understand and debug. They are also more efficient:
"There doesn't seem to be much difference in the way the sharing works"
At first glance they might seem similar, but nested functions are more efficient because MATLAB does not need to search the entire global workspaces to identify that variable, which slows code down: "global variables can decrease performance of your MATLAB code."
"What does it mean that globals "do not allow names to be reused"? And how then do nested functions allow names to be reused, by contrast?"
I find that statement ambiguous, nor do I see a big difference in terms of variable name "re-use". Perhaps some other users can help with this.