This feels like the fundamental core component of what copyright allows you to forbid.
> Everything from ad blockers to reader mode to screen readers do exactly the same thing that Perplexity is doing here, with the only difference being that they tend to be exclusively local
Which is a huge difference. The latter is someone asking for a copy of my content (from someone with a valid license, myself), and manipulating it to display it (not creating new copies, broadly speaking allowed by copyright). The former adds in the criminal step of "and redistributing (modified, but that doesn't matter) versions of it to users without permission".
I mean, I'm all for getting rid of copyright, but I also know that's an incredibly unpopular position to take, and I don't see how this isn't just copyright infringement if you aren't advocating for repealing copyright law all together.