What are the drawbacks of using an induction transformer (step-up) to convert alternating voltage to direct voltage?

It is impossible.

A transformer takes in an AC voltage and changes it to another AC voltage. Up or down does not matter. You can not get DC from a transformer. The power into a transformer equals the power out of a transformer less the small transformer losses. The transformer losses are created by the transformer using some energy to make these changes in the AC voltage. The transformation of voltage is done by continuous coils of wire, bar or plate of conductive material, wound around a core. These coils generate a magnetic flux in a core made of material that can be magnetised. This magnetised core induces a voltage in other coils also wound wound around the core. Without AC there is no changing magnetic flux so there will be no induced voltage in the other coils. The coils that are powered are called the primary winding and the coils that have a voltage induced by magnetic induction are called the secondary winding. The AC voltages in and out are dependent on the ratio of the number of turns in the primary winding to the number of turns in the secondary winding.

Once you have the level of AC that you desire, you can produce DC through a rectifier.

Hope this is clear.