The same issue was just raised by JillMargo10. Please read my answer to her question. I expect there are more home owners considering bathroom designs with the same concern. While this client prefers open shelving, and dries their towels on towel bars after several uses, another would choose doors over their storage niche. For someone else, I would devote more space for a washer and dryer, also an enclosed water closet. I could tile and waterproof all the walls to the ceiling, and provide a central drain, and spigot, for hosing down. I can design and build for public facilities, or clients who want some of those features, but after 20 years, my clients all wish they had more space for robe hooks, hand towel rings, bath towel bars, and towel storage. But, you are correct, closed towel cabinets or linen closets are common requests, as more hygienic with less visible clutter.

Is this shower large enough for a handicap chair?

Yes.