The absolute last thing I need in my browser is AI. What's it going to do, read the page then rewrite it for me to read? Why would I not just read the page? Is it going to generate images of the webpage for me?
AI is a great tool, but it's not useful in every circumstance. Right now product managers are trying to think of any place to shoehorn AI into regardless of it being a good idea or useful just to be able to push out "AI powered!" features. Putting ChatGPT and Claude in a sidebar is absolutely not an innovation. 25 years ago I made a sidebar extension that let you add webcam feeds to a sidebar so you could keep an eye on multiple internet cams easily. It was literally a webpage in a sidebar that you just added the cam URLs to. This is the exact same thing, except an LLM.
I do not need an AI browser, an AI calculator, an AI hammer (it tells you about the nail you're about to hit!), or an AI lamp (it detects when it's dark and asks if you want to turn on a light!).