"They will use that as evidence supporting a warrant to search a suspect's computer" Indeed, you won't be called to court just because your ip address in on a list. There will be further research which could result in: We found this video on the computer which was downloaded from [source] as shown in the logs from with this ip.
Witnesses can be wrong or just lie, paperwork and signatures can be forged.
We can't live in a world where every conviction is somehow "mathematically proved", we live in a world of "beyond reasonable doubt". It's messy and imperfect, but seems (to me) to be better than the alternatives.
I'm not saying we should disregard those kind of virtual evidence, I'm just saying we might need to educate more about the risks of falsifications more.
I mean, it's pretty easy to create a log showing any given IP doing whatever you want. I seriously doubt that prosecutors are demonstrating a chain of custody and immutability in regards to such digital evidence.
If it's the government doing it you at least have the sworn testimony of the investigating LEOs but in civil court it seems like it would be merely the word of the prosecution which is basically no different than, "it happened because I said it happened."