Who will lend BTC when it grows 100% per month? In fiat world people are motivated to invest money because the risks of investment are lower than depreciation of cash. The less money depreciates, the less risky investments will be made. If the money is appreciating, then any investment opportunity must be that much less risky or more promising. With appreciating currency regular folks will not put their money in anywhere, so only very limited amount of resources from professionals will be moved into doing new stuff. That means less misallocation of resources and the products that are really in demand. Since the most growing and promising area is Bitcoin itself and many already have invested a lot in it, the most resources will be thrown in: 1) Bitcoin management services, 2) lobbying Bitcoin-friendly laws, 3) workarounds for Bitcoin-unfriendly laws, 4) wider and better accessibility of Bitcoin.
The OP said:
...and would easily allow one to borrow fiat backed by one's coin stash value.
I think the point is that to collateralize a fiat loan with bitcoin, if the loan goes into default then the value of bitcoin at the time of default is used to repay it. So if you hook one bitcoin for a $90 loan today at 10% interest, and then default in a year when bitcoin exchanges at $180, you'd pay the lender 0.5 bitcoin plus 10%.