I don't see how the claim of 0% interest rate could be a stable equilibrium. If I lend freicoin at 0% interest rate, alternatively I could exchange it to bitcoin and lend bitcoin at positive interest rate. Assuming the exchange rate between the two is stable, then obviously I would choose the second alternative.
As you point out, the lender will try to maximize his profits and currencies can be exchanged. But that also applies to the borrower, who will try to minimize his borrowing costs. That way, bitcoin and freicoin financial markets will theoretically equilibrate and produce the same interest rate.
Now you ask why the equilibrium should be zero interest.
The fast answer is that without an artificial barrier for capital yields to drop, they would drop to zero like all profits do in perfect competition and interest rates are intimately linked to interest rates.
But let's make an example with some imaginary assumptions to simplify things. Freicoins and Bitcoins have the same price.
There's a given market, say car manufacturing, where factories (capital) yield 2% of their producing costs (the cost to build the factory). Of course, their yield comes from selling the consuming goods (cars). Building a new factory would push the yields down, since all compete selling cars. In perfect competition, profits drop to zero, but not yields, since they represent the borrowing costs for the investment. To be profitable with a new factory you need a loan at a lower rate than 2%. Sorry if I'm repeating myself but I want to stress how yields tend to drop by competition, which, by the way, is good for the consumers, since lower yields mean cheaper products.
If lenders/investors can find another market with higher yields they will prefer to invest on that other market first. Higher yields mean that the demand on that market hasn't fulfilled the whole demand at the lowest possible price. There's more margin for the lowest possible price (which is just the raw costs, without profits nor capital yields) on that market so the demand's signal is transmitted to the financial market. But those markets will eventually hit 2% yields and eventually lenders/investors will have to chose between 1.9% or hoarding money.
A bitcoin lender doesn't have any incentive to lend at zero interest, but a freicoin lender has. Borrowers/entrepreneurs will find lower interests on freicoin's financial market, possibly zero. As yields get lower, bitcoin's financial market would shrink in favor of freicoin's. Borrowers don't care about demurrage because they're going to invest the money, spend it on producing goods.
Why an entrepreneur would plan to invest in something that yields 0% ? That means that the factory on its whole lifetime will only pay for itself, not give more return. The lender just wants to spend his money at another time without paying demurrage nor conversion to bitcoin fees. And the entrepreneur is paying his own wage as part of the production costs. Being selfish that could be enough for him. Ideally at this stage the building costs of the factory equal its total outcomes in its productive lifetime and the consumer is only paying for the real costs of production.
I hope this makes sense to you, but of course don't hesitate to ask questions or criticize the parts you don't agree on.