You don’t have to keep tile, but it does help hide any “bathtub ring” around the surface, an it is an easier surface to remove calcium and hard water buildup. There really aren’t other options, it’s tile or no tile.

If you have tile falling off, I’d also look at the expansion line and patio around the pool. Brick pavers often let water collect near the beam of the pool, causing cracking, beam shear and tiles falling off. Removing the water may allow the tile to stay put longer.