Not sure if any of your examples actually shows unsustainability leading to price increases.
Whale hunting stopped when synthetic oils became available and cheaper than "natural" ones. I think the natural ones were still cheap enough.
Coal, and later oil, was a better (-> cheaper) fuel than trees, so people switched. Shipbuilding materials changed as new fuels and new weapons became available. We're not running out of trees, the alternatives were just better.
Sanitation AFAIK was purely a result of scientific discoveries finally being accepted by practitioners, and then by masses.
Horses were definitely useful and cheap enough for transportation - internal combustion engine created a cheaper/better alternative.
I won't comment on natural rubber and wells in cities, because I don't know anything about it.
My point is - at least with some of your examples, there was no strong price increase signal, and thus we can't use them to support the idea that market pressures will always occur right in time to save us.
The original reason for the Jamestown colony, for example, was the high price of wood fuel for making glass. Nobody would have funded such an expensive expedition for making glass otherwise.
Whaling originally was plentiful right off the coast of Massachusetts. These were depleted, and whalers had to go steadily farther out, then into the Pacific, then to the edges of the Pacific. These voyages got longer and longer, and more and more dangerous, and so price increases would have accompanied them.
> Increasing unsustainability leads to price increases
Not if there is nobody alive anymore to raise prices. This theory works well for progressive change but doesn't hold for long-term brutal changes, e.g. maybe historically if people dried the only well in their village there was no price increase (or there was an instantaneous price increase to infinity if you prefer) because the village was doomed.
The development of synthetic rubber was a direct result of high prices and inability to increase natural rubber production.