I paid to remove ads from Reddit Sync in 2014. 9 years went by where I continued to use the app every single day, as ljdawson continued regular improvements and updates (aside from the incident). By the time Reddit Sync went away, I felt I had vastly underpaid for what I got, and purchased lifetime Ultra as a way of supporting ljdawson.
I totally get what you're saying. But at the same time, Sync is so much more than just the content that it displays. The ads are not there to profit on free content, they're there to support the user experience that sync provides. They're also far, far less obtrusive than typical ads
The nice thing is, there's choices! Feel free to use other clients and find what works best
I'm pretty familiar with how one particular brand of TV works, and you're right, it's absolutely not screenshots. It's a handful of single pixels across the screen. By matching these pixels against known content it's possible to identify what was being watched. Not too different than how Shazam can identify a song.
That's not to say all TV manufacturers work that way.