I think it's more about the money and this kind of faith does not bring any money. For the record I don't mind Mozilla's decision.

No. It would have required forgoing most of their current revenue.

The money from Yahoo, now Google, is also a huge source of revenue for Mozilla (if not the main source). DuckDuckGo can't afford to fund the development of Firefox and Google isn't going to throw money at Firefox, if their search isn't the default... Well maybe a little, just to keep a competitor around and avoid anti-trust legislation.

Honestly I doubt the average user would notice if DuckDuckGo was the default, except perhaps for a few rephrasing of a few search queries.