I think I would remove the trim around the entrance. It reduces the ceiling height, and you don't need it.

Pretty home!

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I'm not sure I understand your question. Are you asking if you should get rid of your cased openings in favor of round drywall edges? Because in comparing the two, cased openings are an upgrade. You can trade the colonial style trim around your openings for something more contemporary. But it isn't worth the money it will take to remove your cased openings.

How do you plan to update the trim in the rest of the house? Sounds like a lot of work for not much of a change. If you are leaning toward a more modern look, I'd remove the dark green and chair rail from the dining room In favor of a cleaner, seamless appearance. Good luck with your project.

Removing that trim is going to be a mess. Don't do it. Make decorating changes. Looks like nice home now, just tweak interiors. Big, big project to remove wood, fix underlying condition, feather into exiting walls, match up surface treatments, repaint entire walls around to ensure clean look. Lots more work than you might think. Agree with comment on dining room. Do those type changes.