I've developed my own agent for assisting me with researching a topic I'm passionate about, and I ran into the exact same barrier: Cloudflare intercepts my request and is clearly checking if I'm a human using a web browser. (For my network requests, I've defined my own user agent.)
So I use that as a signal that the website doesn't want automated tools scraping their data. That's fine with me: my agent just tells me that there might be interesting content on the site and gives me a deep link. I can extract the data and carry on my research on my own.
I completely understand where Perplexity is coming from, but at scale, implementations like this are awful for the web.