Wow! You really have no clue how real banks work.
In point of fact real banks DO effectively put their cash reserves online, and most of their onhand cash is frequently in the teller drawers. Have you ever tried to get even $15,000 in cash out of a bank on what they regard as short notice? I have. Somehow or another they misplaced our change order and therefore hadn't gotten extra cash reserves transferred in from the federal reserve. Ever deposited even more than that because the armored car didn't make the scheduled stop for a pickup? I've done that too. You should see the look on the branch chief's face when he realizes you're handing him a Rubbermaid bin with more cash than his branch has in reserves with the Fed.
Here in the US, reserves are generally held by the Federal Reserve. Every night the banks connect to the fed and settle up their account transfers. Since it's mostly all virtual money even though it is dollar denominated this is all very easy. Back in the day it was all done with modems and special encryption cards (which might cost even more than the PC) in a desktop PC somewhere in the bank. These days I expect they've done away with the modems and connect right over the internet just like Mt. Gox.
What protects your account isn't physical separation of assets, but a web of interconnected security measures. First up, being a real, regulated bank, they have proper backup, access, and encryption regimes. Next up, they have constant and ongoing audits to make sure everything checks and balances. Then they have the ability to reverse transactions. And the final security measure is FDIC insurance backed by the Federal government.