Since the voltage in a coil is proportional to the number of turns, the ratio of voltages is equal to the ratio of turns.
So if you need a big increase in voltage, what stops you from having one turn on the primary (instead of a bunch) and then many more on the secondary. Or is this actually a thing?
We wouldn't need as big transformers if so, assuming the current reduction is irrelevant. All I can think of is some kind of power loss or current not being induced.