Leakage reactances are also used, along with core saturation, in the "regulating transformers" of the '60s era, used to produce a clean sine wave at a regulated voltage. These were built both as standalone power cleaners and into the power supplies themselves in early computers (through the start of the "minicomputer" period).
In these the secondary side has an extra winding with a capacitor hung across it to resonate at the line frequency. The flux for the resonance goes through the leak, but the primary and secondary are coupled well enough to "pump up" the resonance (and the field through the leak and secondary) until the secondary core segment saturates, regulating the voltage (and very slightly clipping the waveform).
As long as you don't pull the power out faster than it leaks in (or certain other bad things don't happen) the resonance stays pumped up and the voltage regulated. Short dips and outages are covered by power from the ringing resonant circuit, while spikes get bypassed through the leak and don't have a chance to pump further.
These had downsides: A phase hit could make them go overvoltage for a short time, making things worse than if they weren't there. They were VERY large and heavy, much bigger than a non-regulating transformer for the same power, plus the space for the cap. They burned some power all the time. They had dangerous voltages across the cap.
They were replaced, once high-frequency semiconductors were up to it, by switching regulators, which are tiny, light, and do a MUCH better job of providing clean DC voltages from a range of line voltages, frequencies, and conditions.