How can I cover up my plate rack/cubbies under my kitchen cabinets?

Your cupboards are fairly standard. See if you can get similar doors for that space. Or, put the plate dividers at the top and move the doored cabinet down - no more catch all because you won't reach it!

Have you thought of removing it completely, and using it in some other part of the house, (flip it on its side and use it as a shelving unit for towels, or for gloves and hats, for example) or do you want to keep it where it is so that you can frequently access the items inside?

It’s hard to tell in the photo, but are the openings wide enough for a wine bottle? If so you could add horizontal pieces to make it into a wine rack. Attractive and harder to fill with clutter. :)

If you just want to cover up the area attach a piece of radiator screening or a painted piece of glass. Put hinges on it so you can still use the cubies for what ever but the screen/door will cover the area.

Can you remove the dividers?

What is under this shelf? Counter top? Sink? What are the measurements of the openings?

I think I would store some of my favorite cookbooks in those spaces.

Maybe restyle with cookbooks, plates, platters, etc

I can see why you do not like these, but that area looks removable> If you remove it remember you are going to have sheetrock repair. I would either put doors on the shelf or use as storage for wine, or water bottles. Cook books would work too.

If you want to keep it get some doors or make some to cover it. You can also remove it and use it for something else

I would remove every other divider so you can store other things

As I was looking at the space, I wondered if you could use it for a microwave oven by cutting out the dividers and sliding the oven into this space? If not, use it to house pot lids, muffin tins, or other cooking trays and such. Then get a door or doors to cover it. Good luck deciding.

You can add a drop down door, like a secretary desk.

Take everything out and fill it with items that you like the way they look, leaving no room to become a catchall.

The easiest thing to do is add hinges on the underside and a door that would fold UP to meet the two existing cabinet door with a magnet closure. You could stain or paint door to your preference or even have it covered with a photo/design to add pop of color.

The other option is to see if you can put in some kind of the popular barn door style with hardware on the bottom. Maybe if the doors are thin enough (balsa wood?) you can have them stacked one behind the other?

Is it possible to find additional doors that match your existing cabinets? Or maybe take the dividers out?