It's not just the exchanges that have to have confidence behind them. The exchange (or, at least, some Bitcoin owner out there) has to have confidence in the short seller as well. This is because the short seller borrows BTC to sell on the exchange. The short seller is then expected at some point to pay back the lender in BTC to cover the loan. Because of the additional routes for anonymity that Bitcoin provides, the short seller could abscond with the non-BTC currency as long as they can launder it, leaving the lender high and dry.
As you noted, regulations, law enforcement, and substantial recordkeeping on the part of brokerages keep this from being particularly successful in normal equities trading. If nothing else, a brokerage might require a short seller to keep cash on hand sufficient to cover the short sale, and then call in the debt if it looks like their cash on hand is coming close to being insufficient to cover. (Some brokerages let you use a margin account for this as well, if you have good credit.) The short seller would then be unable to run off with the cash because the brokerage would not release the funds until the short sale is covered. This is a solution that some Bitcoin exchanges might have problems with, because they would be keeping government-issued cash on hand in a customer account as well as BTC, which opens up several other cans of worms.