I'm the same way, I hate using Google search for searching because it's basically useless, and their other ecosystem offerings generally get enshittified over time so it's not worth paying for or relying on.

But if they're letting me using AI for free without logging in and I just need a dumb AI slop answer, then I'm more than happy to burn their tokens instead of my own. Any serious work goes to a different LLM provider. The switching cost for moving to a different LLM provider in the future is practically zero.