In HTML5 Spec, it seems the nested script tags are supported, so what does a real example look like?

In HTML5 Specification, I read this "If the script nesting level is not zero: ...Otherwise, ...". It seems the nested script tags are supported.

But what is a real example that uses the nested script tags? like the below one?

document.write("<script> alert('I\'m in your head!')</script>");  

When used to include dynamic scripts, the scripts may either be embedded inline or may be imported from an external file using the src attribute

Nested script tags are not meaningful because the contents of a script tag must be 'text':

The example given is entirely legal because the 'nested' script tag is simply a text string which will be interpreted when the script itself is executed.

Modifying the document and replacing it's content like this should just replace it's current contents, though I haven't tried.

I don't see any controversy here.