The search box in Firefox has a pulldown menu that lets me choose from 8 different search engines, including Google, Yahoo, Bing, DuckDuckGo, and others. My default is set to DuckDuckGo because I'd rather not be tracked, but if I think another search engine may give me better results for a particular search, the choice is just a click away.

This removes the only real source of revenue Mozilla has. How do you suggest they fund development?

Implement this by having the already built search provider list, with none selected at install. On the first address/search bar use, prompt the user. (Choose or add your own as currently available...)

I like it.

Am I crazy, or did Firefox or some other browser do this around a decade ago? Maybe Opera or Avant Browser, back before money deals were made?

Sounds familiar. Chromium (not Chrome) still asks on first use but IIRC defaults to Google if you ignore it. IE (8, I think, whatever came with Win7) offered an option at first run but I've never had the options page actually load, so it defaults to Bing/MSN.

With what purpose? Surely nobody would voluntary use that?

I would if only to see what other search engines are there.

Fun fact: you can see that without installing a special app. See https://addons.mozilla.org/en-GB/firefox/search-tools/