You might not need ACID during the recording of each charging transaction; however, without ACID, you won't be able to correctly apply each transaction against your account balance during the reconciliation batch processing. Marking each charging record as charged and updating your account balance must be in one transaction, whether relying on the database transaction support or building your own transactional log.
So at the end of the day (yes end of the day processing), ACID is needed.
The account balance is calculated as a function of adding all the debits and credits together. Bank accounts are not stored as some kind of balance value that gets mutated over time. The balance is simply the result of some operation that is cached. It's quite simple. No ACID required. Most of these systems at large banks were built in IMS long before relational databases even existed.
So at the end of the day (yes end of the day processing), ACID is needed.