You could contact a carpenter and see if it could be replaced. The other thing to consider is that wood rooms are being updated by painting the whole room. Or even if you just painted this piece it would update it more than just replacing a few trim pieces.

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Oh wow. What a beautiful room. Is that oak beams? Talk about Good Bones.
Since it looks like you have a beautiful desk there I would treat the built in as a bookcase backdrop. Before I suggest more, may I ask, would you be interested in giving the room a more feminine feel?

See if you can find a furniture maker or at the least, a finish carpenter to come look at it.

The trim and corner blocks that you don't like are probably not integral to the piece, but are added strips of trim that might be removable and replaced with trim you prefer. Worst case would be to fasten new trim on top of the old, but that would make the trim sections project out more.

I have heard that matching old stain/finish with new is difficult.

Yes would like a bit more feminine. The other 3 walls also have wood paneling

Wider view

Show the ENTIRE room please.

Would the entire wall be more useful to you if there were more shelves? Or a closed cabinet? What is the room used for?

I would try painting all the interior back wall panels to match the wall color and declutter the display areas...putting singular striking decor items in the higher openings...use smaller groupings of books with attractive bookends ..maybe remove some shelves for taller openings...for sculptures,etc...(changing any trims would be a huge challenge in matching the finishes)

The center unit shelves could be removed completely (for art or a tall dramatic sculpture)and less shelves in side sections would be more proportionate to the size of the unit ...giving a less cluttered more contemporary feel to the room as well

I love everyone’s ideas but if you want a quick solution that would appeal to your own sense of creativity while you are figuring out what you want to do with this room. You could easily make a few changes and be perfectly happy with it.
Look at it as a bookcase rather than an unwanted built in desk. Styling the whole back drop with a consistent method will ‘fool the eye’ that it is a bookcase backdrop and not an unused desk.
First. Right now, your eye goes directly to the gaping hole at the desk level shelf because it is bigger and has no broken up space as it has no upright dividers. So we visually break this space up just like the shelves above. This will add consistency to all the shelves by deliberately adding these breaks. These visual breaks can be replicated by placing objects that end exactly where the dividers above are placed. You could use tall pieces of bronze vases, or a tall, dark/light spine book. Anything that is tall and thin, like the ones above. But use the same thing for each one. Between these uprights fill the spaces like the others. Books piled high in one. Next to that a curved object. The next one a shorter stacked pile of books. Whatever you like. And keep playing with it by pulling objects from the other shelves and rearranging to create your new composition. Use the order of diagonals for bookshelf styling. This is fun and can be pretty addictive. I change mine 4 times a year at least or whenever I buy a cute, new object in the shops. Also a soft spray of blooming twigs can take up visual space and adds a different texture. I’d also include a beautiful coffee table book of your favourite artist, facing outward, or a framed artwork that you can move directly in front of your printer for when you don’t need to print and when you really want your room to look beautiful. Styling the bookcase as a whole will make it recede if you give the eye something to go to first. Every pleasing visual creation keeps the eye moving by using opposing elements near each other; dull, shiny, bright, dark, smooth, textured. So.
Second. Step back from the bookcase and look at your beautiful desk that really looks great in this space but like a great outfit, it really needs some eye catching jewellery. Add some light reflecting, sparkly objects, like a big, low hung, chandelier over your desk that will definitely stop the eye from going to the shelves. And on your desk, keep the symmetrical tradition of the room by placing a pair of matching Waterford or any pair of crystal vases on each end of the desk, filled with languishing flowers like fuchsia tulips or orange orchids in shiny, metal pots. They will relax, to a tiny percentage, the traditional feel of the room. You’ve now superimposed a light, eye catching triangle shape that jumps to the forefront to stop the eye going where you don’t want it to.
There are plenty of great ideas out there for big changes, but if you didn’t want to change it entirely with contractors and an irreversible paint job this might help. Also, I don’t know know if you are sentimental about your desk but I’m concerned that painting out all the woodwork may make you dislike your desk as it would then be the elephant in the room.
Cheers.

Could a carpenter make drawers or doors for the bottom open section of your desk? Or could you find file cabinets to fit there (wooden ones) or get some that a carpenter can put matching doors on.

Well you've really hit on a hot topic here and gotten so many amazingly different solutions. Have you decided on a plan? I think we are all desperate to know.

LOL .......... "desperate" may be strong. Curious, okay : )