Maybe we use search differently, but I very often don't just want an answer, I want to find a website to help me. Maybe it is because I need to do business with a company and need to find their website to interact with them, or maybe I saw a cool site awhile ago that's relevant to what I'm doing now and didn't bookmark it (because I dropped that habit when Google search was good), or want to read the official documentation about a product I bought, that someone already put a lot of effort into making complete enough and digestible to a wide audience... and the LLM responses tend to get in the way.

Like the parent I use good/paid AI when I want an AI response. So, yeah, an omnibox that knows when I want "an answer" and one that knows when I want to find a thing sounds slightly more convenient than switching between two tools, but Google search is not that Omnibox.