To me its a reasonable trade off, the probability the google DNS server goes down is low and the amount of people who purposely block google dns is also low.
Sure, but don't we reserve the right to run our own split-horizon DNS servers and point fqdn's our devices want to resolve to anything we desire?
Don't like it? Use TLS and verify certificates.
Sure, if the product doesn't fit your need then either build your own chromecast or use different product. I personally do not want to build my own so I'm perfectly okay with the trade off.
I wonder why they aren't just using TLS and pinning certificates? I suppose they probably do, but furthermore want to ensure that they control the resolution of other services (e.g. Netflix) for the device.