The issue then is that no matter what you do with the compression algorithms, the user is downloading these chunks and you can see the pattern of packets in one direction setting up requests and the packets in the other direction replying with the chunks and you can fingerprint what movie someone is watching. It isn't some kind of encoding issue, as the data is all encrypted: it is the entire concept of taking fixed length segments of a movie that will compress to some non-determinstic size. If you take the first two minutes of every Star Wars movie, divide each up into 10 second segments, and then compress those segments, the sequence of sizes of the segments will be pretty unique.
What is so great about this particular paper is that you don't even really need to analyze the TLS layer and try to pay close attention to really figure out the request/responses: they just fingerprint the TCP flow and that's sufficient, which in retrospect doesn't surprise me as what you are really looking for is some kind of rate of requests to responses for the chunks over the course of those first few minutes of watching the video, and don't really need to know for sure where the boundaries are: you have a long enough sequence and a small enough catalog (there aren't tens of millions or billions of videos on Netflix) to get a really strong fingerprint using just the relative rates.
To fix this you really need to either inject extra random traffic (such as extra packets to the server that break up the request rates) that adds so much noise that you can't figure out the signal "in time"--if it takes longer to fingerprint a movie than the length of a typical movie, that's "good enough"--or you need to destroy signal (which is a better description of what we do if the video segments are all the same size: at that point all movies are by definition the same sequence over and over again; if you then pad the length of every movie to the same 4 hour runtime and force the user to download all of the padded black video frames, you essentially 100% solve the problem ;P).
That said, as noted by someone else on this thread, there has been some work done figuring out what people are saying by analyzing encrypted speech packets; but I imagine that kind of technique would be almost impossible to pull off with these segments on the order of multiple seconds long, and including the video in the stream would seem to make that a total non-starter.
Every Netflix client that is watching say 1080p Rick & Morty s1e2 fetches an index of the bits that make up that video, and then fetches the relevant chunks of data.
So if you just fetch that index, no need to "watch" the video, you know OK 1390450 bytes is the 1st chunk of data making up that video, and then 2046917 bytes is the 2nd chunk. When you see that somebody fetched 1390450 bytes of encrypted data from Netflix, they're probably watching s1e2 of Rick & Morty in 1080p. When they fetch 2046917 bytes of encrypted data that confirms it.
So it's "non-novel" but they don't need to (relatively expensively) actually watch the videos they want to match. It's likely any sophisticated adversary has an index of all the common videos from sites like Netflix, the Play Store, Disney+ and so on.
There is definitely more a client could do to make this harder, but there'd be a sharp trade-off where to make it impossible for passive eavesdroppers to know what you saw costs both you and the "broadcaster" a lot of bandwidth, and bandwidth ain't free.
I'd like to see Netflix at least gently stroll in that direction, maybe use some TLS padding to make it a bit harder to do this trick, but I don't expect them to set off at a sprint and ruin their profitability in pursuit of a non-goal.
Off the top of my head: if you took a live streaming approach along the lines of live TV, or indeed Google Stadia/GeForce Now/OnLive, then you could presumably make the traffic patterns invariant over what was being watched. You'd need to ensure the bitrate didn't drop during low-detail scenes, I suppose, similar to what you mentioned re. Skype below.
That approach would of course be far more intensive on server resources, but I'm sure a similar level of privacy could be achieved without such inefficiency.
But in the end it still doesn't mean TLS isn't worth it for all the other benefits (not that you implied that).