Because Google is the easiest search engine to integrate probably. Take a look at this quote from DuckDuckGo:
"Because of the way we generate our search results, we do not have the syndication rights to allow you to host our results on your site (e.g. in a frame). When your users click on the results they will be instead taken to our site."
It seems Google custom search is just the best option.
thanks for shareing, that is pretty intresting and your right google search is proably the best option for quick results.