I agree that if Google is getting the content for free they should, at least try, to keep it ad free for the consumer. But I don’t know if Google has to pay licensing for stuff like PBS. PBS does technically have ads, but they are unobtrusive, shown at the beginning or end of a show and are presented as “Brought to you by….” Less of an ad and more recognition that a company has paid to support bringing PBS to you for free.
I’ve never uses this service, so I’m not aware of how they might insert ads either. Between shows? Typical ad-breaks times every 8.5 minutes of broadcast time? More?
These type of “captchas” look at your browsing behavior. It is sort of a “trade secret” of what it looks for, but it might be screen resolution, mouse behavior, cookies, OS, time to click, etc. Anything a website has access to that would look different from a bot.