Arches are the hottest thing going in high end custom homes. You might want to learn to love them. They add a lot of style for such a simple detail.

Leave them. They add interest and define the separate spaces.

I like arches but I hate pass through windows so I would close the pass through window and remove the counter in the living room.

I like arches and I’m neither here nor there on passthrus. If you like the connection, I would remove the counter and replace it with cabinetry below, maybe that comes to the same height as the passthru, maybe not. It will look more intentional and purposeful,

Keep the arches. They're a lovely architectural feature. Never get rid of such a thing because it's currently "out" -- trends are for pillowcases and tee-shirts, not houses.

Some of us live in areas that have houses with way too many arches in the form of faux Mediterranean houses. Many people that remodel these homes in my neighborhood are removing the arched windows and inside arches to create simpler, less faux-ornate homes. The end results have been big improvements in the overall look of these homes.

I would do something to the arches and/or pass through, but would have to be in the space myself, to decide what those changes would be.

"Would you recommend removing them and squaring off the opening if doing a kitchen renovation?"

No. Everyone has cheap squared off openings. You have upgraded arches.

My 1942 Cape Cod has original arched doorways. I am not sure they are a trend, but just a stylistic choice going back many years. Personally, I love our arches.