They don't need tokens. The bitcoin network needs tokens in order to pay the miners, who are anonymous and scattered all over the world. In a "permissioned ledger" (i.e., a distributed mirrored decentralized tamper-resistant database for a closed set of non-anonymous, legally bound entities), transaction processing would be done by the member entities, for whom the service would be compensation enough; and/or by external contractors, who would get paid in dollars through banks, the old-fashioned way.
Thus a "permissioned ledger" does not need tokens or proof-of-work. It remaisn to be seen whether it will have a use for any of the other distinctive features of the Bitcoin protocol.
There is no doubt that private permission blockchain ledgers will provide a some efficiency gains with their accounting vs other RDBMS merely by forcing the hand of financial institutions to compete and re-evaluate fintech and their processes. I am glad Satoshi could invigorate this evolution in fintech where those that prefer fiat will indirectly benefit.
This doesn't concern me much as to competition with bitcoin as this isn't a zero sum game and there likley will be many competing payment rails networks and currencies.
Ignoring the economic advantages of disinflationary currencies as keynsians would disagree, one thing these permissioned ledgers will never be able to compete with bitcoin on is with bitcoins advantages of being open, KYC free (within the protocol), decentralized, and offering regulatory arbitrage. The costs of PoW are a fraction compared to the cost of regulation and fraud which would need to be managed within permissioned ledgers.
