Yes. Path functionality should enable you to travel along the path easily. The next problem and back to index links on each page are a remnant of a time when no path functionality existed as far as I know. There is however still a problem with the path functionality, it is broken (this was considered a feature earlier) if you arrive at the page from a different than the main page of the path. Until this is fixed the on-page links still have a purpose, when it is fixed I would rather remove them instead of the path (which needs no maintenance work, after all).

Can you explain a bit, which browser coloring you refer to and where you found different URLs (although sth. like this is bound to happen with a manually maintained path)?