Interesting case, with a lot of grey areas. I'd say there definitely are some differences between p2p (i.e. torrenting) downloading and streaming, where in p2p you are also actively distributing the illegal content, in contrast to streaming where you are only a consumer.
There's also the fact that the user has no real way of knowing if the content they're are watching is legal or not (most display ads before, like youtube), heck netflix could stream pirated content and no regular user would really know (not saying they do ofc).
Furthermore, in the case of streaming a clear target is the site that provides the stream, which is a lot easier to target than whatever user ends up watching it.
On the not knowing front, many people used Netflix for 'piracy' either intentionally or unintentionally by watching shows in regions where Netflix didn't have the rights to stream them. I imagine a lot of people simply thought that it was cool that they could get US Netflix in Europe or vice versa.
Interesting the apparent legal (and social) distinction between streaming and downloading, where technically the distinction is mostly in whether the data continues to be stored after it's been watched -- the decision about whether the data transfer is a 'stream' or a 'download' is pretty much entirely down to the client.
And we'll note that browsers usually write the stream to the disk and it stays there for an unbounded amount of time, so streaming is equivalent to downloading [most of the time].
This is similar to the argument made in German law, which explicitly excludes (rough description) "transient copies that only exist as a detail of the technical transfer method" from protection.
AFAIK mostly intended to stop people nitpicking technical details (e.g. claiming that you infringed on copyright on an image that you are allowed to view, but did not have explicit permission to create a copy of it in your browser cache, or javascript in a website, ...), it also is used to defend streaming.
There's also the fact that the user has no real way of knowing if the content they're are watching is legal or not (most display ads before, like youtube), heck netflix could stream pirated content and no regular user would really know (not saying they do ofc).
Furthermore, in the case of streaming a clear target is the site that provides the stream, which is a lot easier to target than whatever user ends up watching it.