Cement board is pretty rigid and has pitting (little holes) in the board. The board scratches real easy and if you are good with a spackle knife, you could easily mud all the imperfections in the board, sand, primer, and then paint.

It might make sense to use concrete board then a sheet of 5/8 fire resistant drywall on top of the concrete board.

Both my houses had just framing around them, one was on an interior wall and other on an exterior wall, then drywall. Of course insulation on the outer walls. There was the space between unit and walls according to code. My new zero clearance has framing within inches of the box and drywall will go right over the studs. The drywall on both fireplaces went right up to the edge with tile surround.

Other than code distances for your studs, I would think the drywall is fine.