It happens in the US too. Any site could have 1x1 iframes loaded with nude pictures of people under 18. If your IP happens to be caught up in their investigation, your computers will get seized, they’ll see you accessed the forbidden pages, and you’re basically done for, especially if you can’t afford a good attorney. Nobody is giving an accused pedophile the benefit of the doubt.

I'd agree that the U.S. law enforcement probably takes a "better safe than sorry" approach to suspicions involving child porn and terrorism, but I think there's a big difference between what's happened in the U.S. vs what appears to happen in Turkey.

Turkey's situation, as described by the OP, is so interesting because it describes the scenario you envision -- in which a government really did go for a sweeping "take no prisoners" approach, in the dumbest way possible using Internet access data.

But FBI sweeps of child porn suspects seem to be very targeted -- e.g. tracing IPs of people who participate in known illegal sites or honeypots: https://www.wired.com/2014/08/operation-torpedo/

Having visited bad sites/URLs/IPs/searches may be used as circumstantial evidence. But Turkey seems to have used the pinging of an IP as the primary way of both finding suspects and the primary evidence for jailing people. I can't think of many similar situations like that in U.S. law. In fact, with child porn, you see courts making the distinction between seeing child porn (i.e. inadverdently) and intentionally seeking it out:

https://www.yahoo.com/news/blogs/sideshow/viewing-child-porn...

https://www.olemiss.edu/depts/ncjrl/pdf/cp%20But%20Your%20Ho...