I would drywall over them.

Have a carpenter add doors to match your cabinets. Maybe a shelf or two. You'll get a ton of storage space.

Either drywall or doors. Just be sure to have that HVAC vent pulled forward.

Oooooh...FUN!

Adding drywall is wasted space. (I'm an organizer!)

Adding doors provides lots of storage & nothing to dust.

Open niches create space for showcasing your individuality -- Arizona history, antique cookbooks, family teapot collection, pottery, large floral arrangements, wine bottles, art, or simply "random" pieces that add fun splashes of an accent color. Here are a few examples for an inspirational springboard

If you want a cheaper or quicker solution than getting a bunch of doors made, you might hunt down some large baskets to put up there , so you can store low-frequency dishwares and supplies without looking at clutter or having to degrease things before you can use them. Should be possible to find some that look decent...