I'm fairly sure the story will hit them with some kind of tragic incident, "I recognize my daughter's hand writing! ", "Did you just refer to your niece using your dead wife's name?", a lost memories arc, or they pretend moving to somewhere else in Japan is like being on the opposite side of the earth.
But even if it does end up being a fluffy, my wife is reborn and re-marries me at 18, then how's it any different from from any other rich dude marrying 18-25 year old and then leaving their house, savings, etc to the wife?
At worst he seemingly has a good enough job that his reborn wife can freely study whatever college subject(s) she pleases without working until he croaks or if she feels like it. The exchange is that yeah, she might have to do the horrific task of caring for her husband in his twilight years.. Just like she would have had she not died before him in the first place.