They capture externalities (true costs) but they have another purpose.

All systems have fundamental constraints. The Earth, for example, has a finite supply of water, air, and minerals. Humans on the Earth are constrained by things like the weather. We cannot on Venus.

However, it would be silly to push the system as close to those fundamental constraints as we possibly can because it would leave us with little room for error. It's difficult to predict exactly how complex systems behave. This means we could find ourselves on an irreversible trajectory before we even realize something is terribly wrong. We need to reduce the risk of this.

Pigouvian taxes (and enviro regulations generally) are just synthetic constraints. We are saying, "If the fundamental constraint of the system is here, then we'll pretend it's actually at some much closer point." This is nice because the system has similar fundamental constraints anyways, so the synthetic constraints are isomorphic but give us a wider margin for error. Overcoming such constraints must ultimately be solved. This forces us to solve them before we're on the precipice of oblivion.