If the TV must stay here, that is a challenge for you to make this corner look it's best. If the shelves are adjustable, I would get them all at the same level, maybe you only need three shelves on each section rather than four. Try to put things in that have some personality. Stacked books with the paper cover removed, sculpture, framed art, vases, plates, bowls. If possible, hide the electronic stuff and wiring, can they go behind the closed doors or could you have a new door front made in the corner that has ventilation if you need it for the electronics? You might think it needs to be painted to give it more life if you do not care for the wood look, or change the green background paint? Consider reducing the number of small framed photos in one area, I notice your mantel is mostly photos too. Try putting the newest photos here, if you have people in more than one photo, put the older photos elsewhere in your home. Leave some breathing room on the shelves and use odd numbers, 3 or 5. Try keeping the area close to the perimeter of the TV open. Inspiration photos attached.

Sorry, the first photo is the wrong one.

I quick answer to determine if they should stay would to paint them. At least if you live with them painted, you can determine if getting rid of them makes sense without a lot of money.
BTW I love the idea of GREY!

Television should relocate. Painting might help a lot. Agree with Merri- try painting first. You can always remove them if you are not pleased with refinishing. The curved wood pieces at the top of the unit date it for me, but even with those painting, new hardware can bring it back to life.

Go! Dated and awkward and just a place for clutter.

Time to remodel...these are very dated!

I would say goodbye to the built ins.