Google provides what they believe to be improved/more reliable services that they can make guarantees about. The open internet is inherently less than that. Besides the paradox about companies owning proprietary technology to key infrastructure that isn't then shared like early internet technology was, one thing is for sure: Chromecast could have made the tradeoff to use 8.8.8.8 a user choice. When in doubt, ask, but with Google, the culture has always been we know better.

This is the same question ask asking why multiple companies make maps. Yes, some may be better, but having multiple means that if someone starts to misbehave (being inaccurate, slow, whatever), a user has alternatives. Regardless of Google not connecting to your personal IP or other PII per your link, DNS is still a business endeavor for them and gives them a considerable advantage to their search rankings. Some people are not okay with that. Note also that it does not suggest they can't use that traffic to show you ads in some capacity.

To be clear, I use 8.8.8.8, but I understand the aversion. Google is a data vacuum, and being forced to give them more data than they are entitled to is a valid concern.