I see your point. Devil's advocate says that they did start as a search engine, ultimately irresponsible for the things they display: they merely process your query and put out what they've found.
The question here is: to what degree are they actually responsible? If you create a platform for people to share things, how much filtering do you do as the owner of that platform?
I think the trade here is user engagement: if you actively fight those who post copyright-infringing material on their services (say, YouTube, though Google the search engine is a big contestant here as well), you're alienating views, and losing views means you lose a part of your audience. They don't want to be seen as infringement-happy platform, so they'd take it down because they have to; otherwise, keep those views coming, and maybe, you'll stay for that another appealing piece of video material we have for you...
Alphabet is the face of what many cyberpunk writers feared back in the day. You can't just sue them for copyright infringement, even if you can make a solid case of them allowing it on their services. You can't fight them at their game, and you can't make your own game, either. They'll play carefully to take whatever they want, and they're too big to fail at this stage. It's exciting a real-world piece of worldbuilding -- but also terrifying.