Phind kinda-sorta did this. For awhile I used it as my primary search, but limitations made me go back to Google. Hopefully ChatGPT's version works very well. Phind was more of a kludge to demonstrate what combining chat AI and search can do.
We're working on a complete redesign of Phind to make it more of a search competitor :) What were the limitations you ran into?
The one thing that kept me on Phind for a lot longer than I would have otherwise been was that I could pay for Claude usage when I over ran my daily quota. With Sonnet 3.5 there wasn't a point since I wasn't getting over the limits for Perplexity and you didn't provide a way to use an api key for Openai models at the time - to this day I find that GPT4 turbo is better than 4o for my use cases. This alone would have kept me around.
Since then Perplexity has gotten worse and they removed a lot of the old useful models. If you have something like poe.com where I can select the model to answer a query and give me fine grained control over the model settings I'd come back in a heart beat - e.g. if I'm doing research I don't know the answer to a high temperature is a good thing, if I want to find bugs in code a low one is better. My current killer feature is something like undermind where complex queries are run in the background and I get reports in due course by email.
Happy to chat more, my email is in my profile. I work in the space and have been building proprietary systems to help ground financial search for two years now.