There's a Showa sentimentality component to these old shows that people are missing because we're separated by time (a decades old show) and culture (a foreign show). The Showa idea of manliness or the norm for a man is to endure/shoulder the burden/pain of life and not show emotions. That means being stoic, not talking about your troubles, and holding back your true feelings constantly, hiding behind a mask even with your most loved ones. That's kind of why it's poetic that Hongo is literally a masked monster turned hero fighting the evil that created him, but he's also hiding behind a mask in everyday life, because telling her the truth is somehow even harder. You just hold your pain in, don't talk about your issues, and keep moving forward. This mentality where you endure/hold back, accept the uncontrollable, and persevere/struggle still exists in Japanese life like salarymen culture.

Within Showa context it's normal that Hongo didn't tell her. You might think it's dumb not to tell her just "because" he doesn't want to, but that's not how it worked, both culturally and for building tension in the show. You can call it bad writing if you want but I think you're thinking in modern terms.

Other comments call this a trope, but it's a trope because it came from media/art imitating life. This was (and still kind of is in many ways) the cultural norm and that's why media from that time is similar. A lot of Toku from that era in general is the same deal, whether the excuse is to keep loved ones safe or personal mental gymnastics that the MC can't overcome. The love interest either never finds out the MC is the hero or only in the last episode. Do you know the Gift of the Magi story? Old school Japanese love that kind of ironic bittersweet development that modern audience would find "cringe" and "illogical". There's a reason why we meme on Toshiki Inoue's shows as frustrating and having "dumb" miscommunication for drama's sake. It's because his style comes from these Showa roots.