The title bar should definitely stay in Finder. The proxy icon is handy for drag-and-drop operations, and can provide important information about the directory tree of the current folder.
Indeed they are, but as I think more and more about it (and I did elaborate on this in another post), I think one simple solution could be to move the proxy icon to the tab itself. They could further display the proxy icons in grey, similar to the sidebar, for a more neutral look.
You could also go all the way "Safari-style" and just have a huge adress-bar, which would display the current folder name (and a proxy icon) when inactive and give you a bunch of options when clicked (including search).
Many ways to keep all the functionality but still get rid off the dedicated 18-20px at the top!