I disagree about the ease of finding inappropriate content. A misspelled website name can bring you to something that is supposed to be 18+.
I know our school had some issues with that type of thing and they changed their filter.
This also more than a few times happened at our kids' first elementary school. I've also seen inappropriate websites pop up a few times based on the phrases in a search rather than misspellings.
The largest challenge for us at home hasn't been those obvious adult websites or obviously inappropriate places etc. The challenge has been how to keep our kids on track when surfing and not wandering off into areas that they really need to have introduced to them by a living breathing human adult, not by watching a video etc online.
Please know I'm about as far from being prudish or conservative as a person can get

- that's not what I'm talking about. The biggest one here recently has been videos posted to youtube by other children - of themselves. Not nude pics or anything remotely "bad" - but vlogs of kids who have been injured in sports accidents - my youngest dd is heavily into sports, so she loves to surf youtube to watch other kids doing sports that she practices. That's actually a good way to use the internet - she can watch technique etc. BUT - by googling "x activity sport x" she found not only those videos, but a lot of links on the side of the screen that go to videos where tweens and teens video themselves and talk in detail about how they were injured during that activity, about surgeries, etc. Again, the videos weren't in any way graphic or scary in an out-there kind of way, but they were scary in a much more subtle way to a kid who is very into her sport and she started worrying about being injured (and also wanted to spend time watching more and more of these videos).
Another example of an issue we've had is with our older dd (middle school) who has a wide range of school topics to research, and with her free-er reaching searches finds topics she is very interested in that are very complex - war, discrimination, etc. All good things for her to learn about, and she is a kid who asks *tons* of questions - which is all good! But if another of my children who didn't ask a ton of questions was landing in the same spots and reading the same things, I'd want to know about it so I could insert some discussion. Opening the internet to do research is very different than opening an encyclopedia back in the days when I was a teen.
My last example is just a silly thing but something that happened when we weren't looking (because we didn't think we needed to be lol). We have email accounts for each of our kids and request that we (parents) know their passwords so we can check how they are using their email. It's really been fine, no content or stranger email issues or anything. We'd used a widely-used provider to create the accounts... but we technically stretched the truth by saying our kids were 13 (or whatever age they needed to be to sign up). We neglected to mention that to our kids, although we've had lots of talks about how sites like FB etc require users to be 13 and there are kids (including friends of theirs) who still are able to create the accounts etc etc. We've also talked ad nauseum about how you never share personal info online. (Which brings in yet another point - don't count on all your kids taking everything you say seriously or actually doing what you tell them to do 100% of the time... but I digress)... anyway our older dd was having fun with all the personalization you can do on your email account with avatars, background etc, and also was really into the "social circles" things where you have friends in your circle etc - all of which was ok - until - she included her sister and updated her sister's info including her sister's real birthdate. Which meant her sister's email account got locked... which meant all the precious emails her sister had from her cousins and aunts were now not accessible which meant her sister was beyond upset... so then dad gets involved (which you would think is a good thing, right?) and being the good dad he is he found a way to unlock the account (in theory) but in order to do so he had to vouch for being responsible for his child's account *and* enter credit card info which he was beyond loathe to do... but did anyway... with the promise from this very large widely recognizable middle-of-the-road company with the promise that would unlock the account.. and it never did happen.
So anyway, that's been our experience - the things that will be of concern usually aren't the things you would have predicted! We have always and continue to request that our kids work on the computers in the open rooms in our house where adults are present and where everyone can see everyone's screens.
Last thing I'll mention - I'd been to internet safety talks by our police department several years ago and found them really helpful. I went to another this spring thinking I'd already have a good idea of what was going to be said and it was 200% different because things had changed that quickly. I can't even begin to relate here all the info that was passed on, so my suggestion is if the police department in your area offers a similar type of talk - GO.
Best wishes,
polarbear