Could yo maybe take a picture from further back right now IMO the copper pies are below the part you would see since the washer will sit in front of the ones I see,

Granted the cover trim....does not look generic so it may be specific based on the layout and the reasoning the plumbing is what it is. Only you can tell so much I suppose, just short of figuring out the runs from underneath, etc, etc....

If you're handy, then just start making some access holes, go into basement/crawlspace and figure out the plumbing sitution and if it allows, then just redo your setup , etc.

Personally, I would be relocating electrical, shutoffs, all plumbing, etc so it's not exposed and it's ~behind~ the laundry machine. Everyone has a different opinion on shut off valves....

My shut off valve box ends about 5 inches below the top of the machine, so if I reach in, I can still turn it off in a dire emergency...I've never needed to, nor have I had hoses explode when away from the house

Could you explain why you want to change it? Functionality, design....

If this is just a cosmetic fix there are lots of easy solutions that do not require touching your functioning pipes. I wouldn't mess with them.

one idea: hang a panel the size of the gap from the cabinet above the washer on a hinge , so it's easy to move but covers the space.

Another idea: take off the cabinets, cut out a notch in the bottom/back of he one above the washer, rehang directly above the machines. Add a nice shelf above the cabinets with some labeled bins or baskets for storing XYZ. Now plumbing is out of sight.

i could go on...

It wouldn't bother me a bit.

Your new washer drain hose will have a U bend holder that will keep the end of drain hose in a tighter U and it will just hook into your drain opening, no need to obtrusively loop way up and back down as the current one does. Your washer shut off surface mount box is a standard item still available at Home Supply Centres at least in Canada, not sure if I saw it branded as Aqua-Dynamic or Brass Craft or Waltec or ? I would also leave as is, maybe use some GOOF-OFF to remove the handyman on-off markings if that bothers you. Plug your new washer in to a plug-in surge suppressor, unplug when not in use and turn off the faucets after use. You and everyone else will be noticing your new washer, not the shutoffs and drain hose.