This obviously isn't the case for everyone or else my grandpa would have treated his wife with a lot more respect.
You perfectly described my grandpa Alfred and my grandma Ferne. But, I do see it very differently than you do.
At a certain point in his late 70s or early 80s, his girlfriend of a very long time passed away. I don't know how long they were together, but it was at least 30 years. Now the way I see it, that's a marriage.
The topic of his girlfriend came public within the family about that time. My mother had been whispering about her for awhile, so I knew. My little sisters, I don't know. Probably not. Grandma knew the whole time.
Grandpa and grandma grew up in a society which understood that strong men with good incomes often have more than one woman. My mom was an aggressive college-educated Feminist who had a terrible marriage and a very awful rocky dating life before it. She never accepted that she was her own problem. She inverted my father's household and lorded over him. He was miserable and always hiding away in the basement.
She spent a long time trying to convince her mother to divorce her father. It was pretty trashy. Her mother loved her father, and he loved her.
If we lived in a Biblical society, if my grandparents grew up in a Biblical society, our grandfathers both would have just had two wives publicly. Instead, the public condemnation and inverted nature of the society we are in kept them in a situation which could have caused them shame if they were to live honesty. The social arrangement we have rewards secrecy and silence. A major part of the problem is that in this inverted society, nobody cares if a married man has a girlfriend on the side. Even men in the churches do it. But wives expect the husband to be silent about it. It's about social status, "what will my friends think about me?"
My grandmother liked to play the victim. It was a big part of her identity, she wouldn't have let it go. Her husband was a very good provider, respected in his community, others looked up to him. He was well respected. When his girlfriend died, people just felt sorry for him for losing her because it was known that he loved her.
I was part of a conversation with my two uncles, his sons. They were talking about it. The one uncle told said to us "dad told me he never cheated on mom and I believe him." That was the effeminate uncle who had been divorced by a masculine mean wife of his. I don't know what the other uncle was told.
During that visit my grandpa took me for a walk in the orchard. He didn't talk about the woman or assume that I knew about it. He instead told me that a lot of men have "a woman on the side." He said "everybody does it, but nobody talks about it." Now I don't think that's true but I think it's generally kind of normalized. It's the wrong way to live.
The Bible doesn't talk about "cheating." It talks about adultery. If a woman is married and another man sleeps with her, both of them shall be killed. Zero tolerance for a man taking another man's wife. I don't know if my grandpa's girlfriend was married or not. If she was, then he was Biblically doing wrong and should have been punished. Not because of my grandma, but because of the husband who he would have theoretically wronged. The problem I have with it is that he should have married that other woman and lived with her in his home alongside my grandmother and lived an honest life with his head held high.
My grandfather treated my grandmother with a high degree of respect. She was well taken care of and he let everyone know how much he cherished her. When she passed later, he was completely distraught. He was one of the strongest men I knew and he was suddenly unable to take care of himself for quite a while.
That might not be a very helpful story but it's what you reminded me of.