DuckDuckGo doesn't really have their own index. They mostly just fall through to Google and Bing for their actual results. It's cool they supposedly don't track you, but they are really just a proxy rather than a full fledged index themselves.
Bing/DDG has the site indexed correctly, and I get a decent amount of traffic from them, but Google's market share is large enough that it's not really feasible to just ignore them.
(And I'm not buying ads on either one, this is about organic ranking)
If OP's potential users are Google users, optimising for DDG (bing) won't do anything. The fact is most people are using Google and if you only care about DDG you are throwing away most of your potential visitors.