Reap what benefits? DDG on its own isn't a formidable search engine compared to the rest of the playing field.
If Apple built their own proxy, they can gather more data points about their users in the way they want. 1st party user data is very important to future innovations. I'm not sure why you would even try to make a case that 3rd party data is more important than 1st party.
The money that google is paying Apple to keep google search as the default. The stronger DuckDuckGo is, the more leverage Apple has to negotiate for even higher prices down the road. It’s rumoured to be 9 billion today, it could be 10 or 12 next year.
It is therefore in Apple’s interest to prop up Google alternatives in a way that makes it believable that the company might switch away from Google after all. You lose that leverage the moment you have your own search engine, because why then wouldn’t you favour it over all other alternatives?