So on the contrary, Bitcoins are a deflationary economy. Deposits will have a negative interest rate (ie: holding your money in a bitcoin bank will correlate to fees), and borrowing BTC means you only will have to return bits of it. (ie: if I borrow 100 BTC from you today, I only will have to repay you 75 BTC two months from now).
It is only fair, as people learn to expect BTC to keep growing in price.
I don't think its a very healthy economy to be in, but its a completely different endgame scenario than what you describe.
Interest is almost* always non-negative. I'll only lend you those 100 BTC if you pay me something more than I'll have if I didn't lend them.
That makes a BTC based economy more prone to hoarding, and less prone to investing (what is clearly a bad thing), and also more prone to hoarding and less prone to spending (what economists think is a bad thing - I have no idea why).
* The exceptions to this rule are not systemic, normaly appearing in times of disruption. You can't base an economy on them.
That said, plenty of people are "banking" with online BTC wallets. Instawallet, Coinbase, etc. etc. The economics for these services work against them, and they are hopelessly doomed to failure.
Your reply actually raised more questions than it answered. I get that high interest rates are bad for a market that is built mostly on credit and I can kinda-sorta see how that would slow down an economy. But I don't see how that completely eliminates investment.
At some point, people have to exchange goods. People have labor to provide and goods to sell and services that they need provided and goods to buy. How is credit the only thing that enables that? Or is the argument that only credit enables it at the level that we see in current day capitalism?
The central bank prints money. That is a fact. What people forget is the fact that this is useful to an economy. The central bank can abuse its power, and inflate away your cash holdings. (ie: print too much money). That is why BTC are pegged at 21 Million coins.
So the question now is, what will an economy based off of a heavily depreciating asset look like. What are the risks?
Would it be better to have government responsible for most investment ? I don't really care about consumers hoarding their cash - they'll buy the things they really need or want. But I am concerned if investors are better served by hoarding than by demand deposits or any other kind of debt instrument. This could drive up interest rates to unprecedented levels. Higher interest rates mean higher cost of goods and thus higher costs for consumers.