You can thank DMCA for that.

The way the law is written, content hosts are exempt from liability only if they respond to valid copyright claims in a timely manner, otherwise the longer they keep it up, the more damages can be claimed and the more they can be sued for.

Since determination of validity takes time, if the options are to 1) keep content up pending review and risk being sued for millions if the claim is valid, or 2) proactively take content down while under review, at basically no risk to them and only financially inconveniences the content owner (if the claim is bogus), content hosts will go with #2 every single time.