And I misspoke about the bang syntax: it actually runs a search on the target website. If you search for "foobar !g" on DDG, it redirects you to this page: https://encrypted.google.com/search?hl=en&q=foobar. Same as "kitten video !yt" redirs to https://www.youtube.com/results?search_query=kitten%20video.
edit: I misread your comment about goog's site search indexing vs a site's native search. That is entirely site dependent. And it's still only a "kitten videos site:youtube.com !g" away in DDG.
What seduced me was the reasons stated by my grandparent comment (and the fact that good ol' Google search is a "!g" away).
Not everything has to please the mainstream. Discussing whether DuckDuckGo is a good name is one thing. But to questions the features of the engine on account that it's not "mainstream" misses the point. I think.
http://scholar.google.co.in is not meant to be a mainstream product.
Where as http://google.com/search is a mainstream product. And DDG thinks itself as Google's competitor with a heart for privacy, that's their USP.
So yes, as far as DDG is concerned, mainstream matters. It's a generic search engine, not a vertical for scholars or the like.