[Yoda]

...by definition an angled hinge will fly higher than a horizontal hinge.

Sorry, Jim...t'ain't necessarily so!

Horizontal Hinging has only "one hole in the sky," i.e., the Clubface Closes Only.

Assuming Angled Hinging (some Clubface Layback) or Vertical Hinging (only Clubfaced Layback)...

Pick a hole!

With Angled or Vertical Hinge Action, the further back (Up Plane) you locate the Ball, the lower the Ball Flight. In contrast, the further forward (Down Plane) you locate the Ball, the higher the Ball flight.

So, Horizontal Hinging offers only one trajectory for a given club in a given set of Clubs. In effect, 'one hole' in the sky. Only with Angled or Vertical Hinging can Trajectory -- higher or lower -- be effected.