They are either canned from the LOA with the IFR facility, relayed
verbatim from the IFR facility (4-2-4), or the tower controller is
trained, certified, and delegated the authority by the appropriate
level of management to use the tower radar display to issue them
(3-1-9c).


Exactly. In the first case, the tower is not capable of tracking the
aircraft with respect to obstacles, and therefore cannot provide any
terrain clearance, which is why they can't vector.

However, in the latter instance, where you have a radar tower, they
CAN vector aircraft, if certified to do so.