It’s not about “ownership” it’s about “interest”.
You do not own your house (assuming you are married) you have an interest in it.
If you left your wife and bought another house. You would have to pay 2nd property tax on your new home. (As did I). If you subsequently fully transfer your interest, within the time limit, you can claim it back.
If you don’t you can’t.
It is emerging that AR has a nesting arrangement and this likely includes a lifetime right to live in the home. That is an “interest”.
Sorry not sorry you are wrong, as usual.