If you ran a separate PE from the transformer XO to the ground bar of a TT system you would then have a TN-S system which are considered the most safe and advanced of all systems today. A down side might be higher fault current yes, but if an RCD failed to trip in a TT system you would have an energized grounding system, both a shock/electrocution hazard and a fire hazard. It this reason why some electricans like to put 2 RCDs in series on a TT earth. Running a PE from the XO to the buildings grounding system will clear a fault no matter what, even if an RCD failed.
TN-S or TT, its always a good idea to have your foundation bonded and to have ground electrodes.
Yes these terms are not common to the NEC or CEC but IMO these are terms that many forum member should know since its the correct way to describe power systems through out most of the world.