Browsers have been improving rapidly now that there are multiple strong players with significant market share. Wouldn't it be great if the search engine market were more like that?
Mozilla is in a unique position to be able to improve competition among search engines. We're not a search engine company and we stand for meaningful user choice.
If Mozilla were to decide that improving search competition was important to us, here are some things we could do:
Measurements and surveys
We could run Test Pilot studies to learn about search engine choice, speed, and result quality. A study could even encourage users to try multiple search engines and report their experiences.
The content and order of Firefox's search bar have always been determined exclusively based on what we believe to be best for Firefox users. We should strive to have the best data possible when we make these decisions.
Ease of experimentation
We could make it easier for users to compare search engines. For example, after I enter a query into the search bar, it would be nice if I could run the same query on another search engine in one or two clicks. The Search Tabs extension is one example of how this could be done.
Ease of migration
We could let users share their search history with a new search provider, so the search engine they've used in the past doesn't have a hidden personalization advantage.
We could require special promises from search engines about how they will use data shared through this feature. For example, we could require they only use the data for result personalization, and only on the search engine site itself.
There may be ways to use history to improve search quality that involve only partial history sharing, such as client-side relevance tweaks or RePriv. If Firefox supported one of these methods, users could comfortably ask their search engine not to store any search history.