If 99% of what you do is in a browser then the browser has really taken the place of the operating system. And browsers are destined to follow a similar path to the OS. Remember when windows removed the full file path from explorer?
I don't know what Windows version you're running, but on the Windows 8 partition on my laptop, it shows the full path with prettified separators, showing the plaintext when you select the path.
And that same way of doing things would work quite well for a web browser, IMHO.
There are many annoyances I have with Windows, and Windows 8 specifically. That is not one of them.
I remember when they split the full file path into clickable pieces for each directory, making the fully-visible path even more prominent and interactable than before.
In Windows 7, if I go to a folder in my home directory, it doesn't show c:\users\sp332\Downloads\foo instead it shows sp332 -> Downloads -> foo. The c:\users part is removed.
Your user directory is a browsing root, along with "Computer" and "Favorites" and "Network". From whatever root you pick, it will always show the entire path if there is enough space. If you browse to the same folder from C it will show "> Computer > C > Users > sp322 > Downloads > foo"
So that's just some multiple mount point weirdness, not removing the path.