In a transformer, the ratio of voltages is equal to the ratio of the number of windings on each coil. So in theory, a transformer with 1 and 10 windings should be equal to one with 10 and 100 windings. Most transformers then should be able to be reduced to have one coil with only 1 (or at least, very close to 1) winding.
I would think this would be beneficial, because less wire means less resistance. Why, then, do many transformers have many windings on both coils? (my experience mostly comes from taking apart TVs and microwaves. I don't know if this is still true for power grid transformers)