In the case of the banks, their regulation by the state is a recent phenomenon, as is fiat money itself. So we can look at what happened before when banks were more independent. I'm no expert on the subject, but it doesn't seem all that attractive - as the article mentions, crashes and panics were a regular feature back then.
People had a healthy mistrust of banks and also means to store money outside them (precious metals). The bank panics didn't have lasting damage, recovery was fast and they didn't get bailed out by the government. Perhaps government control has mitigated against these little panics, but it set the stage for real meltdowns and slow recovery afterwards.
There are two distinct functions banks do: money storage and lending. These can be completely separate. You only need a money store for the convenience of not having to carry metal. Nowadays, you may want an electronic store as not to have to carry cash.
As for lending, that is a function much older than banks themselves. You don't need consumer deposits to lend money. Some banks do operate that way, but there should be a more clear distinction. We could have 'vault banks' and 'lender banks'.
Both 'vault banks' and 'lender banks', or combinations can operate in a free market.
You can store currency or gold in various non-interest-bearing ways in the current free market. It isn't a very attractive option compared with banks, however as stored money (metal-backed or otherwise) that isn't lent or invested necessarily loses value on average, in the long term against currency that is.
we can look at what happened before when banks were more independent
Don't confuse correlation with causation. I think de Soto makes it clear that it wasn't the banks per se that caused friction back in the old days, but rather the lack of comprehensive, accurate, and accessible records.
There's always going to be winners and losers, bubbles and busts, but governments playing a role in monetary policy only exacerbates these problems. Recoveries come in spite of intervention in the economy, not as a result of it. See Rothbard's The Panic of 1819 for an example from the early days of these disastrous ideas: http://mises.org/resources/695
