Depends on what room it is, but closed in storage space sounds like a good idea.

pretty baskets or bookshelves with one of those rolling ladders

Unused/rarely read books! Pottery collection ... hardy house plants ... mounted natural displays (seashells, branch art). It's hard to tell your decor style from this pic.

We use a similar over-closet alcove for fun seasonal displays. We had an outlet installed, wired to a switch in the closet, that is especially useful at Christmas. We also put LED tape lighting (another switch in the closet) to light up whatever we decide to feature. Between holidays, we feature pottery or other artistic pieces.

You could have it drywalled. Everything placed up there is just a dust collector IMHO.

What are the dimensions? Would it be useful as storage space? What would you store up there? Seasonal displays sound nice, but will you care to get up there multiple times a year? And if you use the space to display things, you will still need to get up there periodically to dust.

Looks like a narrow shelf, not really enough space for storage.