It's actually quite simple...we are looking at 3phase half wave rectification here.

The insight about the inductors over heating is correct....IF it were not for the pulsing circuit on the primary winding. (usually it's straight DC)

The result would be smooth rectified waves...that then have an off time...the practical result is square wave in nature.

Notice the inputwave form...then notice what the inductor/diode does to the waveform (doubles it).

With the overlapping waves of rectified 3phase...the ripples in the xformer would be insignificant (and would heat the primary winding quickly), much like straight DC across the primary...not until you shut down the power and the inductor collapses would the xformer create power in the secondary.

Transformer action can be viewed in physical terms using the eqn. of power. This eqn is...

The change in work (changing magnetic fields...as they must perform work to establish) / The change in time (this being time on and time off of a pulse)

It should then be obvious why sharp on/off times produce huge voltages....

Lets say we put in a set amount of energy to perform work and make a field in opposition to Earth's field/Aether....lets say it's 5 "units"...well then lets say the change in time is say...1 second.....5/1=5....Ok, lets say we can drop the change in time into say...1 millisecond....5/.001=5000.....every time the change in time gets closer and closer to 0 the power rate reaches closer and closer to infinity. Try graphing 1/x on a graphing calculator and see what happens...it's says error in the data table at 0, yet the graph is correct...the asymptotes reach infinity at 0

Anyway, hope that makes sense about the overlapping waves being essentially straight DC, and the need for a gating/pulsing circuit in the primary