I’m seriously contemplating it. It’s an eye sore to me

If you paint the whole wall the same color, it might help the ledge disappear.

never understood those things. Does this house happen to be in AZ, they seemed to love doing that in the 90's

First check the positioning of your overhead light fixture in your entry/hall where this is located. Will the light be "off center" or otherwise oddly placed;

... if so, add changing that to your anticipated cost.

... if not, add a cabinet above the protruding wall rather than just walling over empty space. Use "hidden" doors -- doors without a knob or handle on it -- let it look like a wall above the bump out is just a wall. You might consider having the new wall over the new cabinets have a wood panel look similar to the appearance of "wainscoting".

RL Relocation LLC- nope not in AZ. KY in 2007! I don’t know why.

LOL!!!