This expression is more symbolic than to be taken at face value.
> meaningful enough - OP
this means there's an optimum
> Given more animals that produce sounds, the ones that can transmit more information - OP
This means animals below (a?) optimum threshold. Shannon called that threshold the bandwidth, I believe.
> [complex sounds] take more energy to recognize
So this is the other side of the equation. We have a signal to noise ratio that limits the bandwidth. Energy is Information and Energy conversion, ie. Information transmission is inherently lossy, because Entropy decreases in closed systems. The trick then is to use the information to expand the frame of reference, to grow as an individual and as a species. That gives a lower bound on what information has to be converted into the system - that's what OP is talking about.
> What specifically will kill you if you transmit less information
In the limit, not transmitting any information means heat death. So, OP was talking hyperbole, obviously. The question for a local optimum is obvious - birds proliferate and not in a small niche. A global optimum in the infinite, infinite bandwidth at some point, or infinitely increasing bandwidth in infinite time are obviously out of scope - even if we like to dream on cosmological scales. Hence, OP's leading statement is rather symbolic than to be taken at face value.