You've conflated the role of assets and currencies in a financial system. Even separating that out, that's not a productive asset. The productive asset would be an interest in the lending platform.
Concretely it would be like treating gold as a productive asset because InteractiveBrokers lets you take out a margin loan collateralized by your gold. Gold remains unproductive in this scenario, IBKR shares would productive. Value from lending would accrue to IBKR shares.
I guess I was listing the value of what crypto has.
What does "productive" mean? If something has somekind of value/property that is useful somehow, then isn't this "productive" in the sense that it produces that value?
Concretely it would be like treating gold as a productive asset because InteractiveBrokers lets you take out a margin loan collateralized by your gold. Gold remains unproductive in this scenario, IBKR shares would productive. Value from lending would accrue to IBKR shares.