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.
RE: Steemit & google search: a curious choice for site wide search.