Convertibility gives asset owners a guarantee that they can convert their assets into state money when they can no longer find private takers.
State money is unique in that it is the only form of money that retains its nominal value. This is because it is backed by the coercive power of the state, and it is the only currency that can be used to pay taxes.
For financial assets, convertibility is more important than durability, and is an effective substitute. It allows holders of these assets to lock in past gains before the market no longer values them.