I wonder "which" Catholics want that.
I'm afraid that I would call them "stupid Catholics." They sure don't speak for ME.
Christians DO take care of "Mary's house" (a simply one-room, door-less, stone house) in Ephesus. It's where she died. Remember when Jesus consigned her care to John? "Behold thy mother..." John had gone there to preach the "good news," with Mary.
It's NOT written in Scripture as it is just "history" so perhaps many Protestants won't believe it.
https://en.wikipedia.org/wiki/House_of_the_Virgin_Mary