You can get in the kb/s range over a couple of kilometres. You don't have to drop to tens of bits per second until you're trying to transmit over many nautical miles.
Examples: https://geo-matching.com/uploads/default/b/e/benthos-modem-p...
Being to push a handful of ints every few seconds is more than enough for a lot of cases, especially if the "modem" (radio?) is cheap enough.
to me, anytime underwater communication is concerned, it is solely to be in the realm of military submersed vessel communication. There's no compelling reason for any other communication to undergo the expense of underwater transmission.
As you said, there is a lot of noise that needs powerful error correction to be used, such as how the Reed-Solomon code was used in deep space communication. Prepackaging information before relying on wireless communication is usually the most necessary part of any reliably complex system.