You don't need to look at their internet history. You talk to your kids about safe behavior. Then you're somewhat around when they're using the computer/device (until you feel they're of an age where that's not needed). The very knowledge you might see their screen at any moment will moderate behavior.

And properly working parental controls don't let the kids install another browser without permission.

I bought my niece a Chromebook for a specific purpose (she needed a device to do vision therapy with). I installed FamilyLink on my phone.

In FamilyLink I went through each setting and put everything as restrictive as possible. She can't install apps. Only the vision therapy website is whitelisted. If she tries to go to a different website or install an app it gives her a prompt letting her ask an adult for permission.

You don't need to be a software engineer to do any of that, you just need some basic reading comprehension. Eventually when she's older I can make things more permissive.

Now that said: the FamilyLink software could be much better.

It seems to be mainly designed for kids on android phones, not chromeOS Chromebooks. None of the screen time monitoring features work. I can lock her Chromebook but I can't see how much time she spent on it or set time limits on apps. I can't put a time limit on the Chrome browser (or any default apps). And if there is a way (outside of adding the device to an organization like a school does w/ Google Admin/Workspace), the documentation is not great at saying so.