So do I think the 'layman' cares? Yes and no. I think they care that they get good search results, I don't think they care where they come from. As pg points out building a replacement search engine is a Hard Problem(tm). You can make a competitive search engine with just 15 - 20 million dollars, but displacing the existing player is more nuanced.
This is something Bing knows all too well, they effectively created a clone of Google's search capability and they only pull in about 30% of the market. Blekko has been steadily adding share primarily by not being the same as Google, rather we've added specific features that were valued by different segments of the market (we're still the only search engine that lets you completely turn off ads as a user preference for example) but mostly folks just use what ever the search box provides.
[1] Note that both Yahoo and Bing are effectively the same search engine as Yahoo is 'powered by' Bing results. http://www.comscore.com/Press_Events/Press_Releases/2012/6/c...