Entirely depends on the TV IMO... I have no issues installing third-party YT clients on mine.
If people would rather pay money for the convenience, that's fine, I'm not going to stop them... that's what all software is anyway, even FOSS. Every abstraction layer in computing is just another level of saving time.
Nobody gets upset because your C or Python program wasn't written in Assembly, and then claims you're "just coding for convenience." Or when you use someone else's library.
Or, you didn't build your own house brick by brick... and make the bricks yourself, etc.
The principled position behind "you should install something" is that in the scenario you outline, you cannot just install something, and this is a kind of power over you that you are relinquishing to both YouTube and the TV manufacturer. You will not get it back.
If it's fair enough for Youtube to send me a video full of ads, then it's fair enough for me to run a program that removes the ads. The only way Youtube's business model actually works is either a) people watch the ads voluntarily, or b) they are able to force your computer to not do what you tell it to and instead to show you ads. Because all computers are general purpose computers, option b allows the server to impose arbitrary restrictions on you, not just reasonable ones. You might think watching ads is ok, but future restrictions (like fiat banning you from otherwise public content) might not be. That's the argument.
Of course, if everyone used an ad blocker then Youtube's business model would not work. But businesses are not entitled to a revenue stream.