When a site receives a takedown notice, if it complies, then the content will actually be removed from the internet. From the point of view of the notice's submitter, this is the best outcome.
If the site doesn't comply, then a notice can be submitted to search engines to de-list the site. The content is still available, still infringing, it's just fractionally more difficult to find.
If Google demoted sites for complying with notices, it would be a very powerful reason for those sites to stop complying.
I see your point, but practically speaking, for most people removing from google.com is removing from the internet. You can't visit what you can't find. So there isn't a fundamental difference between the two types of takedown requests given the dominance of a single search engine.
Given that, I imagine that copyright holders file takedowns where it has the quickest effect, either directly to the site or to google.com. But this is just a technical difference. It seems odd that it should affect search rankings, and it feel more wrong given that Google owns a major target of takedown notifications, so this isn't just Google objectively settings things in order - it has a huge inherent interest and bias here.
When a site receives a takedown notice, if it complies, then the content will actually be removed from the internet. From the point of view of the notice's submitter, this is the best outcome.
If the site doesn't comply, then a notice can be submitted to search engines to de-list the site. The content is still available, still infringing, it's just fractionally more difficult to find.
If Google demoted sites for complying with notices, it would be a very powerful reason for those sites to stop complying.