Nobody could cheat secretly. They'd still cheat. The framing story in my favourite comic issue "Winter's Tale" has more or less exactly this be scenario, "I was going to tell you" he says. The people in Winter's Tale and most of that run (Gaiman's Golden Age of Miracleman) live in a utopia, but they're still people and they still cheat and lie. The larger point of the story is that children won't fill a hole in your heart.
Your last point is exactly poignant; it'll be lawmakers who end up above the law, above the control. Which makes it more like 1984 than a "borg" utopia.
The solution shouldn't be to make crimes easier to hide. It's to legalize homosexuality.
Indeed, I believe the first use of the "Right to Privacy" was by a lawyer and Louis Brandeis, and future Supreme Court Justice, upset that a journalist had written that one of them attended a wedding.
Depending on who brings to suit, I expect it's likely that even the conservative justices will suddenly agree with a right to privacy.