But what happens to the bank's asset value if TBills are suddenly no longer liquid (or at least desired)? Wouldn't that trigger some kind of valuation crisis, since banks are required to maintain a certain level of asset value?
Perhaps even more important than strict valuation is that banks (and especially institutional investors) have strict rules on the type of investments they can make. One of the most important issues is the level of risk carried. T-bills have historically been considered a (or the) risk-free asset. Suddenly they are not which potentially leads to a lot of selling (lowering prices) or attempted selling (if markets freeze).