I think you can make an even stronger statement:

"A distributed consensus ledger can only survive if it is successful as money."

Note that Bitcoin did not solve the Byzantine Generals Problem because that problem is unsolvable. Bitcoin made it so that any successful attack is uneconomical. That only works if bitcoins are valued as money.

This means anything that tries to replace Bitcoin's functionality will either do so by being better money or else won't be a distributed consensus ledger.