We all know that G's site command is a useful tool to show how many pages our sites have listed in the index
No, we all know that it is broken. So very, very, very broken.
Does the site: command show what pages G thinks are important on your site in the first positions?
This is an interesting question. I've tried profiling som sites using the site:- operator, but it doesn't seem to be useful. Unless you combine the operator with a search phrase, in which case you will see what pages do well, for specific terms. IMO that is more useful, since if a page ranks well for a term, which is relevant for me, i would rather get a link from there, than from other pages.