I would remove it and for additional storage contemplate removing the soffit and adding more upper cabinets. I would also have a larger island with storage and potentially seating as the space would turn into an open plan great room.
If you don't want to do a full-on kitchen remodel, you wouldn't lose that much cabinet space if you took down the wall but left the bottom cabinets and reconfigured them as an island. But if you are still in need of cabinet space, you can consider an open shelving unit that doesn't block the view through the rooms (like the second attached photo but in a different style to match your home).
A little off topic, but I think some beams like in the first photo I found while looking for examples of partition walls with vaulted ceilings would look nice in your home.
In the first photo, the wall doesn't stand out as much as it seems to in your case. Perhaps this is because there aren't staggered heights or because it spans the width of the vault.
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