We use 5 1/2" baseboard. If you' re using 2 1/4 "casing", I suppose you
could ask the drywall guy to run his knife/mud along the bottom edge

That defeats the purpose of the 1/2 inch gap, a break from the floor if it
gets wet, keeping the drywall from getting wet, deteriorating and
developing mold.

DONT drag the mud down onto the floor. Keep it ON THE BOARD, 1/2" above
floor.