Why using a High and Low side driver in BLDC?
Couple of things. Your "brushless DC" motor is an AC induction motor and your three phase motor driver is what makes it appears as a DC motor to the outside world.

You need high and low side drivers to produce some sort of AC to the motor windings and especially to create a voltage difference between two adjacent windings.

Hypothetically, you might be able to pull off some kind of push-pull scheme with only low side transistors but since you can't interface your logic ports to the MOSFETs in the motor driver part of the motor driver, you are going to need gate drivers anyway and they in turn can be interfaced to normal 3.3 V logic (I assume 3.3 V on your behalf).

IR2113 is a good start. Datasheet here: IR2113. Or the L6234 if it's low voltage and you want everything integrated.