There is no reason whatsoever why a fractional-reserve banking system couldn't be built on top of Bitcoins (which would then serve as the banking system's base reserve currency) in exactly the same manner as the existing system was originally built on top of a foundation of gold (and, to a lesser extent, silver). Of course, today most of the banking system is built on a foundation of nothing but faith in the American people not to debase their currency - a faith which is beginning to look rather misplaced.
See my post at https://forum.bitcoin.org/index.php?topic=22553.0
So, really Bitcoin does nothing whatsoever to eliminate the practice of fractional-reserve banking, but in fact gives it a stronger foundation, by eliminating the need for banks to trust sovereign fiat currencies, or physically ship gold & silver around to settle accounts. At best, it only makes it more difficult for banks to charge exorbitant fees for wire transfers (since "cash" Bitcoins can be sent essentially for free).