Remove and drywall IMO no good use .

It's adding nothing. I would remove it completely and drywall as suggested above.

Remove it.

How about to make it flush with the wall like in this bathroom

https://www.houzz.com/hznb/photos/bathrooms-modern-bathroom-new-york-phvw-vp~147424083 

I think it has value - a small amount of added storage space. A hand towel in a recessed area might be hard to reach. What about leaving framing and placing open shelves for decorative items. I personally wouldn't drywall over it.

My builder fitted mine out in the same walnut wood he used in the vanity and the cabinet.

We drywalled over ours and I'm happy with the decision. It's a lot more contemporary without it. If you really needed more storage you could recess a tall narrow one behind the door if your studs allow for that placement.

why do people hate medicine cabinets??
I would keep it. I think they're really useful.

I agree, anj_p, that is why I made shelving of the old small one and added two large ones. The amount of stuff they hold surprised me.

You can take it out and put in one of these shelving options. All different styles and colors. https://www.concealedcabinet.com/shop-now/all-cabinet-styles/14x18-white-recessed-sloane-wall-niche-w-plain-back-and-one-fixed-shelf.html

We just installed one of these that looks like a picture frame. We needed to move the opening a bit though to make it work as a place where one would have a picture hung.

https://www.concealedcabinet.com/shop-now/recessed-concealed-cabinets/

What did you decide to do?