square them up, not down. make sure your carpenter understands. otherwise they'll look very low.

i mean by square up to make them the height of the top of the arch; cut out the corners, don't fill in the arch. i expect they are framed with a square header at the top with the corners filled in.

but i will say i do like them as well. just didnt want you to end up with them being lower than you imagine.

There is already a header over all the arches, most likely, so squaring it up shouldn't be too much of a deal. If you intend to take the walls all the way to the ceiling, then you should still be all right. You need to talk to more than one contractor.

Arches are a design choice. They are not indicative nor prohibited in any style or period of architecture. What I am seeing in your home is visual occlusion with all the openings giving the rooms a cave like feel. Your contractor will tell you what walls can be eliminated or altered. They will also tell you what walls will require a larger expense and need a support and/or header so your house won't fall down.

I would leave the arch from the entry to the dining area and remove the entire wall that separates the living room - the 2 larger arches in the 1st image. Then to keep continuity leave the smaller arch as it won't look chopped with that wall down.