I don't know of any data that isolates the energy cost of transport and storage of cash. Transactions are tricky, you could use the salary of the worker for the 5-15 seconds (or however long the handling/counting of cash takes) and equate that to cost of electricity.
Given a retail worker might cost a business $.03 per minute, you are looking at 1c per transaction. Now let's look at BTC. At 9GW when I looked at it, it was processing ~4.5, lets say 5, transactions per second. A kilo-watt-hour (kWh) of electricity will wholesale for 6c. If we are doing 5tx/s, that's 18000 in 1 hour. 9GWh to do 18000 transactions
(9,000,000,000) / (3600 * 5)
Gives us, 500 kWh per transaction, at 6c gives us $30 per transaction.
You might be able to argue subsequent cash handling might take a few minutes per transaction handles, but even so.
So given cash transactions save at least $20 per transaction, cost of transport and storage IMO would be negligable. These costs drop further with something like credit card transactions.
The two biggest problems I see with BitCoin and most PoW currencies (and I'm going to single out BitCoin) are;
1. BitCoin has a maximum transaction speed well below what is required for a world (or country/more localised) enconomy, 7 Tx/s doesn't cut it. VISA apparently does well over 1000+.
2. As mining gets harder, and as the network tries to reach the theoretical transaction speed limit, energy usage grows even more out of control.
9GW is such a massive amount of electricity at the moment. Even as solar + wind + storage becomes cheaper to build and capacities grow, it'll still be a huge amount of electricity and there usage by the BitCoin network will only grow. This is more electricity usage than the state of NSW in Australia _generates_ most of the time. That powers the residential and commercial electrical needs of a 1st world state with 7.5M people.
I think the more cheap power that is available to currencies like BTC, they'll keep using more and more with diminishing returns.