Thought experiment: 

- Be a completely regulated Ecash custodian
- KYC your customers as hard as you can
- Make them authenticate for every ecash transaction
- Log everything in your database
- Know how many users you have, and what their balance is

With all this, you can still have: 

- Instant payments with zero fees
- Offline payments (no internet required for payer)
- Anonymous payers, authenticated receivers
- Programmable ecash (spending conditions)