forgive me if this has already been said

the DO only allows the TP to be used by his most trusted servants. Moridin, Sammael i believe at times. Why? It's such a powerful tool and it can't be sensed by either male or female channellers. rather than it being a privilege to wield (which it is) maybe it's more about the fact that the DO trusts the wielder not to abuse it. you can't channel in the DO's presence, perhaps though you could surprise him with a TP attack.

this would coincide with rand swapping bodies with moridin. he gets the TP and blasts the DO in that place where you can't channel. turn back on the DO his own weapon this means no saidin/saidar corruption

:edit: or use the TP to create a new prison/seal