Note: This question may seem really pointless, but it's actually in the context of a cryptocurrency idea I am developing, but I posed it this way as the question is not really about cryptocurrencies at all, but rather the impact of a bizarre monetary policy on exchange rates.
The Republic of Nowhereland follows a rather peculiar monetary policy: new Nowhereland dollars (NWD) are created by destroying an equivalent number of US dollars, at a fixed 1:1 ratio. Anybody can go to the central bank with any quantity of USD, ritually burn it in front of a bank official, and receive freshly printed NWD. In fact, NWD banknotes are inscribed with text saying
100 Dollars, Sacrificed to the Gods, at the Central Bank of Nowhereland
or some other denomination. Even the central bank itself is strictly forbidden from creating NWD without destroying an equivalent amount of USD.
Otherwise, the central bank does not interfere in any way with the foreign exchange market, and NWD is fully convertible in every sense. The government does not even have significant foreign exchange reserves.
My question is, what sort of implications, especially on the NWD/USD market exchange rate, would such a system of currency issuance have? Obviously, the NWD will never be valued significantly above the USD, since otherwise burning USD at the central bank would be profitable, and the supply of NWD will rapidly grow until it's no longer profitable to do so.
On the other hand, assuming the Nowherelandish economy grows more than it contracts, it seems like a NWD priced significantly lower than the USD would be unrealistic, as in this case the money supply will never grow. This would cause the NWD to appreciate until hitting the 1:1 ratio when burning NWD becomes profitable again. Also, it seems like this would be anticipated by forex traders, so everybody would buy NWD whenever it's cheaper than USD, so the NWD would essentially be pegged to the USD.
Is my reasoning correct, or am I missing something major? Why are there no real-life currencies backed by such a "one-way" currency board? It seems like it would allow currencies to be soft-pegged to another currency, without incurring any obligations for the central bank to buy its own currency at a fixed rate.