[Someone]

If you manage to tell the other party how compression format X works, you can use it after that, and send information faster and using less energy (if we’re talking interstellar communication, broadcasting likely takes way more energy than any message preparation does)

If you intend to send lots of data (which, as you point out, you will have to, to give the receiver any chance of making sense of it), that may be a net win, even if you spend lots of time getting there.

You could, for example, teach that the bit pattern of ‘=‘ signals equality by sending simple math expressions

  .. = ..
  . + . = ..

and later try to convey how run-length encoding works by reusing = in that context

   aaaabbc = 4a2bc

Easy for the receiver to figure out? Absolutely not, but if you give them a chance, they may figure it out, and if the alternative is that you can only send a third of the data, that may be the better choice.