Then use search engine and believe in misconception of those results being unbiased and possible to find

Chatbot with set of answer generators won't do it on your behalf.

And you can have this choice with "AI", just write one with open and transparent dataset.

With crowdsourced open "AI" you would have too, given enough drilling from your side.

What you are trying to imply is that in search engine you see the results, whereas in "AI" you don't have presented where it found that information. So those should be presented in "AI" and the problem will be solved.

The point is, you already don't have that choice, there are pages which are indexed so low, you not gonna find them.

AI can also be crowdsourced and managed in the same manner as search engine. Problem is bias is inherent to both of them. Webcrawler which indexes webpages for search engines with weighted algorithm giving your search engine results, and "AI" crawling web to find those resources for you (replacing natural language into query for weighted algorithm) is basically the same.

Read about SEO and answer yourself if you can index your website high in the ranks so easily. Most of search engines results ranked high are paid, so therefore are "officially approved sources".

Regardless of which, the term AI in this context is highly overused.

I have a strong feeling that there really isn't a choice and there is no free search engine nowadays. It's not viable for anybody to do that for free.

Whole business model of most of currently existing search engines is based on presenting you results which will point you into direction of their business partners, buy stuff they produce, etc. That's business model of Google, Bing, and many more.

Compare search results of those two mentioned above. Then add duckduckgo and see