Like let's say you're a network admin of a college with conservative religious views, and you want to see if anyone in the dorms is watching "immoral" content. You probably can just intercept an entire unencrypted session and replay it on your machine and see what it was. But you don't really have the funding or access to expertise to develop a side channel attack yourself, and there are no off-the-shelf devices that will do this for you, are there?
Encryption is likely the difference between your management saying "Show me what the kids are watching" and "This isn't worth assigning our network admin to spend half a year on effectively a cryptography research problem."
(Incidentally, encryption may also be what allows a sympathetic network admin to refuse an order from their management, which is also worth considering in your threat model.)
I think it's true that if you had either the resources of one of the richest handful of countries in the world or access to some talented grad students etc., you could do it. But if you're even a non-rich country (like one of the many small countries with moralistic governments that censor the internet) it seems harder, and if the goal is spying on what people watch, it's unlikely that people talented enough to do it will find this a problem they're happy to volunteer their time to solve.
(This is a genuine question - the attack might be much easier than I think!)
TLS fixes a whole lot more than just privacy, it's also authenticating the remote end. Are we really suggesting dumping something that is trivially accelerated in hardware to do some homebrew crypto crap just for the sake of a forum thread?
Netflix solution is fine, and the concentration of interest in TLS means it only gets cheaper over time to build Netflix-like configurations, which is especially great since we've spent the past decade or more trying to convince the entire industry this configuration is also best practice
But yeah, you’re right. You could glean a lot of information from nothing but a collection of movies’ exact runtimes, as visible from the network stream. Although that wouldn’t tell you much about a single movie, given enough viewings you could make pretty good guesses about which movies someone is watching.