In my opinion, having linen storage next to the kitchen is a beautiful thing! I would work on improving the appearance of the cabinet with fresh paint and nicer hardware, however, if you'd like to visually open up the space, remove the upper doors and patch the hinge holes before you repaint. You can either still store linens there (if you're really neat!) or use it as a display case for china or glassware.

Don't remove it - have the drawer "slides" replaced. A local cabinet shop / carpenter can retro-fit with Blum slides; many different weight capacities, full extension option.

https://www.cabinetparts.com/c/drawer-slides

Consult a carpenter. The drawers can be planed or adjusted to allow them to slide freely. You may even be able to retrofit them with modern hardware that would allow them to soft-close. The carpenter may also be able to alter the upper doors to add glass. To me, built in storage is one of the details that give an older house substance.

Because of its proximity to the front door and it’s apparent central location, it could be a very convenient and organized drop zone. If you‘re able to bring power to it, you could use it as a centrally located, easy to get to, but not-on-the-counter place to charge and store a phone, laptop Or iPad. You could use the drawers to store your purse, briefcase or backpack, an umbrella... I’m sure you get the idea.

Have a professional carpenter change the glides on the drawers. He/she may even be able to remodel the drawer section into four shallower drawers. If you don’t have a coat closet, the whole interior of this storage unit can be changed into a coat closet with two narrow doors. I wish I had a great linen closet like that in my hall!!

Congrats on your new house!

I am going to be the odd man out but I would try to find a way to remove the whole thing, providing you have ample storage elsewhere.

This built in is not unique, interesting or a defining feature (to me) and it seems to suck up a lot of space.