So I am going to say, for the technically inclined its time to chase down your router firewall logs and find where the TV is going to for ads and block the IP or port range. Would be curious what the TV does, properly engineered it should just act as if its not connected at all.
This would not be without precedent. Some Samsung TVs already refuse to exit setup mode if they can't connect to the Internet after initial power-on to geo-lookup their IP to make sure that they're being used in the country they're sold for.
The best solution for streaming is a low-end PC with hardware video decoding and the ability to run Ublock Origin.
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Edit: I see from other comments that Samsung TVs already go into degraded functionality mode if they can't connect to their ad servers, and already serve some ads from endpoints used for necessary functionality.
I still use my Chromecast for Youtube, because the UI in a browser isn't great for couch use. On the CC, multiple people can add videos to the playback queue, I haven't found a good replacement for that yet.
For anything longer than a typical Youtube video, it's not an issue finding a movie and starting it from a wireless keyboard.
Our current TV is a 42" LG that I got for free from work. It's old enough to not have any "smart" features, it has no networking at all. The picture quality is great and no ghosting unlike a lot of older LCDs. I am not looking forward to the day I eventually have to replace it.
I just found out this weekend; with an older, cca 2013-ish samsung tv, connected to a network that has OpenWRT router with Adblock, and forced redirect of all port 53, 853 traffic to the local resolver. It cannot resolve its mothership (the rules were already in the Adblock list, I didn't add anything). The TV shows up a messagebox that it cannot to the Internet and asking the user to check the connection.
The local DLNA sources work.
However recently I wanted to setup my home automation system to automatically turn the TV off when I go to bed or outside, and for that I needed to connect it to the home network.
I solved this by confguring the router firewall to drop any package from the TV to the internet. It works!
Integration brings unneeded obsolescence and reduces choice and control. May be hard to avoid in space constrained phones but should not be needed on tvs.