The use case of "I have a big pile of data and I need to ensure that it survived transmission intact" isn't going anywhere. Just being in an analog computing world would not make the way some data needs to be precise go away. Not everything is a TV signal being consumed by human eyeballs.

But if you want an even better exercise, sure, work out how to send, say, precise stock market transactions where a "$5.04" becoming a "$5.05" is a very big deal to some people who have lots of money, and work out a mechanism for verifying the integrity of a lot of such data efficiently.

Bear in mind "efficiently" in this case includes the idea that "$5.04" and "$5.05" are actually close together, not separated by quite a lot of signal bandwidth. It should be of a similar size to the current digital world where that is a single bit; if you're throwing more bandwidth at your representation you've already lost to digital. Or to put it in analog terms, that needs to be pretty close to the noise barrier already; it's not a solution to make it so that you end up with "$5.04 +/- 0.000001" and "$5.05 +/- 0.000001" as the two signals you send. That is, after all, what digital is in the first place: All signals are analog in the end, and we send 0s and 1s with enough separation that the receiver can then re-amplify them into a 0 or a 1 without loss. It's not really analog if you're not hard up against the noise floor, it's just digital wearing an analog wig.

If analog is supposedly "better" than digital... at least, for the sake of argument, I recognize you did not make that claim... that would include being able to do some of these things that we do in the digital world quite comfortably. If it's just a niche... well, that's exactly where we are now in the world anyhow.

Quite a lot of real-world data is quite digital in nature. This message I'm posting is intrinsically digital. Even if I were to write something by hand, we all know, and knew even before computers, that the essence of that message is captured by a stream of letters. When we read the Gettysburg Address it doesn't even occur to us to worry about the theoretically vast amount of information we lose by not having the handwritten original. While those can be of historical interest we all know the payload is in the digital stream of letters and words. You have probably never worried before about whether the nuances of Hacker News posts are lost because they're typed in a fixed-width font but displayed in a proportional one, because the digital text carries the vast majority of the content. Even in an "analog world" there is no escape from quite a lot of digital-characteristic data. And there is no escape from the many, many issues with truly analog solutions, such as the inability to copy data without loss. This text has undergone literally dozens of copies by the time it gets from my keyboard to you eyes, and that would drive the analog world insane. Either accept much more degradation than any of us are used to, or dedicated much much larger amounts of bandwidth to everything in a way we would find horribly inefficient in our real world.

Un-0: Generating Images with Coupled Oscillators