That is why both an oscillator and a storage element such as a capacitor or inductor is required to "hold" the output voltage long enough until the next cycle of the oscillator recharges them through the transistor and Vin. Tweak the timing and the amount of energy stored in these elements and you can create a multitude of voltages and current outputs.

You can’t make a buck regulator without an inductor.

 

The inductor is needed because it can limit current and drop voltage without any dissipation. That is where the savings come from. You can use a resistor in place of the inductor in a hysteretic oscillator, but its dissipation will be the same as a linear regulator.

 

one of the ways that switching regulators increase efficiency is by reducing the time the main transistor has current flowing through it (the main heat source on a purely linear regulator)

The efficiency is increased by the transistor operating as a switch, where it dissipates little power when the current flows, rather than in the linear region, where it has to dissipate the power due to the load current times the difference in voltage between input and output.
The time the transistor is on has little to do with that.