Honestly, the whole going out of the house thing is just straight delusion.
Hanyu is one of Japan's most famous men. If he announces he's married, everyone will be looking for a wife and trying to find out who she is even if he's as vague as he was. Eventually someone will figure out her identity regardless. Hanyu has to be naive to think otherwise. His wife and sister were keeping her at home to avoid harassment is not a reasonable solution. Her identity would still come out, and he'd just look like a jerk who doesn't understand how to have a relationship.
The better answer to this would be to a) never announce the marriage in the first place and try to hide anything (as they'd apparently been able to hide their relationship up to that point) or b) make your marriage public and turn yourself into couple goals so the fans will fight the paparazzi battle for you.
There was a jpop star who, at 19 and about to have a few projects centered around her, got knocked up by a guy who was 27, less famous, and who had only been dating her less than a year. This was an idol - someone supposed to be virginal and pure and not date anyone. It was quite the scandal both because of the circumstances and because it ruined the projects she was working on (involving other people). They got married and she took time away from stardom. Then she returned to blogging, became a mommy blogger, developed a few merch lines for moms and babies, and got both herself and especially her husband more famous than ever on television. While people including the tabloids criticized their relationship at the time, 16 years later their instagrams and YouTube channel make them one of the most popular couples in Japan to this day. The tabloids try to dig up stuff, but the worst they've found is neighbors complaining their kids are spoiled and too loud. One time tabloids brought up that the couple had arguments - to which they gained more fans by stating the shockingly healthy and mature way they handle their arguments. Their fans are some individual fans, but a lot of fans of their family as a whole.
Yuzu could've gone that route. If you've got nothing to hide, sometimes it's best to not hide it - tabloids live off of hidden secrets. But he didn't, and it made things messy. Maybe he was worried about the fan backlash?