Nice of you to correct me, and maybe ledger isn't the right word at all considering that most of their transactions are credit based, but do you really expect me to believe that Visa contacts JP Morgan Chase to verify credit hurdreds of thousands of times per day?  I'm simply saying that Visa is keeping track of a lot of data in order to process all those transactions.  It may be pruned regularly since the banks have to provide statements and whatnot, but some transactions take a few days to clear, so they certainly have to track it that whole time.  Regardless, none that changes the fact that they process and track a lot of data.  Moreover, my point that storage is the cheapest part of a miner's arsenal still stands, and as long as miners are paying the kind of money they currently pay for ASICs, storage is not going to concern them.  On the other hand, income obviously will, and IMO, when the block reward halvings get relevant, more transactions are more likely to keep bitcoin secure and competitive than higher fees per transaction and users that go to sidechains to avoid paying the fees (and that's even assuming someone as genius as Satoshi comes up with a good trust-free way to make sidechains serve this purpose instead of all the purposes sidechains were really meant to serve when the concpet came about).