The problem is solved if Joe is allowed to pay his debt in an asset other than BitUSD.
No it isn't. How should it work?
1. Ana still has 500 bitUSD and relies on the settlement guarantee, i. e. she expects to be paid $500 worth of BTS whenever she wants to cash out.
2. The blockchain has created the bitUSD from thin air. It can only destroy them when they are paid back. If Joe pays his debt in BTC, then the blockchain can't burn the BTC, and even if it did the bitUSD would continue to exist.
I agree with your analysis that with many people sticking to their bitAssets instead of trading them the system can't work if the collateral is in a downtrend. However, BitAssets come with the promise of stable value. With that promise, it is only natural (and perfectly acceptable IMO) that people buy and hold BitAssets when BTS is in a downtrend.
What's missing is an appropriate incentive for BitAsset holders to sell their holdings, thus reducing the debt. The
original design of BitAssets came with two such incentives, both of which have been effectively scrapped by now:
1. MSSR - a large MSSR rewards holders for selling into margin calls. Because this mechanism leads to a premium on the market price (and because it is expensive for debt holders), MSSR has been reduced further and further, which has improved the peg but also removed the incentive to sell into margin calls.
2. Global settlement aka Black Swan - global settlement is like a Damocles' sword pending above both BitAsset holders and debt holders. It sets a limit to the promise of stable value, and thus provides another incentive for BitAsset holders to sell their holdings, because if they stick to them for too long they will start losing value. Thanks to Global Settlement Protection, this threat has been muddied and partially removed.