Well... all of the benefit to the user. Google doesn't get to use your DNS requests to sell ads.
How do you envision this working on the product in question? When are you ever making arbitrary DNS lookups in a Chromecast?
Seriously take the tinfoil hat off for a minute and think rationally. Google owns the entirety of the software on the device, and all connections to & from it. There's nothing they gain in terms of data harvesting from hard-coding their DNS here. There is no user input in play at all here. What are they going to harvest from a device that only ever does DNS lookups for their own hostnames?
If this was happening on Chrome, or Android, or something where user input & interaction was actually a thing then sure. But this is a goddamn Chromecast. All it does is watch YouTube and similar. How in any way, shape, or form can those DNS requests in any way help sell ads?
i.e. I suspect Google force their own DNS so that one cannot so easily use e.g. PiHole to filter out DNS lookups for servers that stream e.g. YouTube adverts.
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My initial reaction to the post above was "ship a known-good DNS if you must, but honor the user-chosen service unless it's not answering." This makes sense as a more common reason you'd want to hardcode a DNS, and a reason to honor your setting over whatever is coming back from the customer's DNS.
I still can't see a good rationale for only using the hardcoded DNS, though. Not only does it strip user control, it opens the door to all kinds of secondary stupidity like breaking every Chromecast in Turkey by insisting on a blocked DNS.