Who determines the value of nature? Would you be satisfied letting a market do that, instead of a centralized authority?

The fact that “money” is still involved has nothing to do with this argument. Even the Soviet Union issued currency.

What determines the value of anything?

We do it the same way we do with everything else:

> The economy of the United States is that of a highly developed country with a mixed economy

> A mixed economy is variously defined as an economic system blending elements of a market economy with elements of a planned economy, free markets with state interventionism, or private enterprise with public enterprise.

Getting back to your question:

We establish a market for this, guided/corrected by state intervention if and when needed.

You can actually quantify the specific impact that loss of shoreline has on tourism, fishing etc.

Fundamentally capitalism isn't about pricing things, it's about growth and extracting a profit.