Their marketing and brand are the most important aspects. Bing proxies are a-dime-a-dozen but only DuckDuckGo has achieved tremendous media attention and funding.
One of the proxies had to win out, right? We're only talking about DuckDuckGo and not BearBearClaw because they survived. I don't think they're doing anything particularly special. They're also a much older company with a lot smaller search volume than people realize.
Their marketing got me. I was duped.
So I could just make a DDG?
If you are willing to spend a decade marketing privacy features and bashing the establishment, yes. They are not Google-style "tech disrupters". One could say their success is as much a product of Edward Snowden's revelations and the subsequent societal shift towards tracking-as-a-liability as much as actual technology. Don't get me wrong, their UI gimmicks like !g are nothing to be scoffed at. UI has value, just ask Robinhood and Stripe. But DuckDuckGo is certainly not "hard tech".
You sure could. But DDG is a decade old company and its total lifetime searches amount to less than a week's worth of Google searches so it's likely your efforts will be in vain.