On the other hand, like sysadmins who enjoy reviewing network logs to find which married executives spend their days skulking around Grindr there are a lot of parents that abuse this to become straight-up voyeurs. There's even an episode of Black Mirror about it. Regardless of your moral/religious convictions, you really don't want to discover or become party to your kids' sexual proclivities without cause.
I don't bug my kids' devices, but I did have to resolve a sexual harassment issue with my own daughter. Her behavior was starting to become worrysome-- lengthy secretive sessions on her phone, followed by signs of distress, anxiety, not eating, etc. When she didn't have access to the phone (or the battery died) it was even worse. So I black-bagged the damn thing, found out what was going on, and confronted her only on the nature of her behavior ("you haven't been eating lately"), gently guiding the questions toward what I knew to be the truth ("is someone bothering you?") and letting her do the talking.
She's none the wiser, the problem got resolved to mutual satisfaction, and I don't have to continuously violate her trust or privacy.
Not sure what you do when they realizing you're watching them and then just get sneaky about it. I remember being sneaky. I assume my kids will be sneaky.
In other words I think having some kind of anti-virus software on their computer or tablet, that logs the websites they visit, the articles they view, is totally fine.
The problem is that many parents aren't very subtle when bringing up sensitive issues, causing anxiety and determining the child to hide in the future. And I don't have a good solution for it — my son is only 8 and I'm still thinking how to tackle such problems.