Obviously all browsers rely on direction from the user. But they also typically rely on instructions from the browser maker's servers. Traditionally, you get all of those instructions in a single download that's been pre-packaged (the browser program itself). But if part of the browser's logic requires more computational resources than most consumers have, what's the problem with "outsourcing" that bit to Perplexity's servers?

As a consumer, I don't think it's very prudent to trust a company with that kind of access to your data, but it doesn't seem materially different from the kind of trust you have to give to Chrome.