We actually have two money systems that are used on a day to day basis, cash and accounts. Bitcoins replace cash, but accounts are where the real magic of the economy happens.

Lending -- as an institution, as opposed to as an individual -- is all about fractional reserve banking. The bank pools the money of its depositors and lends it out without restricting the ability of the depositors to access their money. This increases the money supply, and generally works OK because of a combination of (a) most people not needing most of their money most of the time and (b) a lot of transactions happen purely through the bank's internal ledger, without needing cash at all. If Alice writes a check to Bob, who immediately deposits it, the bank just updates their ledger and it doesn't matter whether they have cash on hand to cover it.

There's nothing preventing you from operating a traditional fractional reserve bank using Bitcoin instead of cash, and it would work the exact same way as a traditional bank with exactly the same advantages and problems. But if you're writing checks for Bitcoins instead of dollars which end up being processed entirely through a bank's internal ledger instead of through the Bitcoin network's blockchain... why? How is that really Bitcoin?