High current low voltage transformer not working
Primary inductance, if it's coupled completely to the load via the secondary, does not limit the current through the transformer, it limits the magnetising current.

Leakage inductance, enhanced in the case of a microwave oven transformer (MOT) by the magnetic shunts, decouples the primary and secondary coils, and limits the current.

In a MOT, the purpose of those shunts is to make the feed inductive, to resonate out some of the series impedance of the capacitor in the voltage doubler. This improves its efficiency.