R&D of this sort is funded best with a strong profit motive, unless the government is willing to shell out for it.
In order to work on pie in the sky ideas, you need to hire brilliant people for long periods of time, with low certainty of success. And this is expensive, and corporations will not generally do this out of the kindness of their hearts... the stars align sometimes where the private incentives and public interests are the same.
Xerox PARC, Google X, Bell Labs, and so forth meet this description just as much as DARPA.
But the traditional direct profit motive is an important piece of the engine of progress, and relying only on this other incentive structure would cause stagnation.
The definition of open source might include such a thing, but a project that originates from a lone genius rather than a community is not what is usually meant when people speak of open source.
That is great for many things, but for something like self-driving tech, it is already being used in cars on the road. This is not just experimental, it already has people's lives on the line. That is a lot of trust in something that is not available to be audited.
EDIT: Lorkki's comment explains part of my thoughts on it well. Other companies subsidize open source project that exist at the core of their business. Is there a difference here other than scale? If so, what, and how would it change the situation?