I can only fathom "viewing illegal streams" leading to arrest in the case of CSAM. Regardless of any staffing or resources, it's a complete travesty to arrest anyone for using their internet connection to view lawfully produced content.
The power to restrain the physical liberty is a substantial corollary of the state's monopoly on violence, which should be employed when those arrested are a menace to other peaceful citizens.
I could see law enforcement getting involved in copyright crimes committed by commercial pirates, issuing fines to consumers or identifying them to the rights holders who can then seek redress in a court of law.