The whole point of Arrival was that we had to learn the alien language. The purpose of their arrival was to teach us their language so we could help them in the future.
Had the purpose of the aliens been to spread the knowledge of their culture then it may have made sense for them to analyze and learn our language, but since that wasn't their goal it wouldn't have made much sense.
In pretty much every alien encounter movie it's the humans working out a plan for communication from scratch. You'd think the aliens would put a little more effort into it, especially if they've been spacefaring for years. And if they haven't, wouldn't they be a lot more curious about us?
I would love to see a cinematization of Robert Forward's Dragon's Egg, which I think gets this right.
Messages don't exist by themselves, but are layered. Eg. To understand that a radio signal is a video I need to also understand video protocols, RF communication, etc.
In GEB, Hofstadter talks about the Three Layers of Any Message:
1 - The Frame Message
2 - The Outer Message
3 - The Inner Message
He uses the example of a "message in a bottle" washed up on the beach. The "Frame" is the recognition that the bottle is sealed and contains a dry piece of paper. The "Outer Message" would be the fact that the writing on the paper is in French, and the "Inner Message" would be the actual contents of the French writing.
At each stage, the reader needs to have some set of concepts or language with which to grapple with the nested messages, if they have any hope of finally decoding the Inner Message.
For example, a wild boar wouldn't recognise the Frame Message in the first place, while a German person might recognise the Frame Message, and recognise the Outer Message ("This text is definitely French"), but be stymied by an in-ability to actually read French.
How will the aliens even know they are looking at signals encoding video and audio? Do aliens have technology and knowhow in the RF regime? Will they even be able to receive, store, or analyze the TV waveforms? Do they have the notion of amplitude and frequency modulation? Also, how will they know that the signal encodes video? Absent ground truth, low entropy (or equivalent measures like bigrams, Markov models, etc.) is the only way one can determine that a sequence is a language. Even if they are able to convert the RF signal to some low-entropy sequence of symbols, there is a very real possibility of them going off on a tangent: mapping the information to a completely different language.
A real world example is the symbols of Indus valley civilization. Several decades into the information age, and about a century since the seals were discovered, researchers haven't even conclusively established that the symbols encode a language.
Which is also something interesting to consider. Death is probably less bothersome if your perception of time is non-linear.