Some things are so simple that it takes a while to understand them. For me until now, one was the question of how anybody could lend money and not expect interest - for centuries, usury was forbidden under both Christian religious and civil law. In France, interest was illegal until after the Revolution in 1789 - see here.
And then the penny dropped, so to speak. If the supply of money is fixed, and the economy gradually becomes more larger and more efficient, then money gradually becomes more valuable, as The Mogambo Guru explains here. So if real GDP grows at the rate we seem to expect (on average, about 2% per year), then with a fixed money supply, a depositor would earn 2% in real terms, as would a lender. All you would need is adequate security for the return of capital.
Banks would have to cover their running expenses (I believe Swiss banks already do charge depositors for holding their cash really safely), but this would be need to be in the form of explicit costs, which might therefore be better restrained. Borrowers would have no reason to keep switching loans; in fact, the need to charge arrangement fees would act as an incentive to remain loyal to the existing creditor.
But it looks to me like it would mean the end of fractional reserve banking, inflation and periodic banking crises, not to mention the permanent and pervasive importance of money lenders.
Would that really be so bad? If so, then "if you can't beat 'em, join 'em" - would you and other like-minded readers care to join forces with me and start another bank? It seems to be the only game in town.