It's probably worth pointing out that the 2^-16 chance is per invocation of the protocol.. it's not an offline attack. So you'd have to be reeeealy patient to run it enough times to give the attacker a decent chance of success.
The best attack I can think of would be for me (or someone who's camped out on my rendezvous server) to make an MitM attempt on like one out of every 100 connections. Slow enough to avoid detection, but every once in a while maybe you get a success. Of course you don't get much control over whose connection you break (if you did, you'd be back in the detectable category again).
FWIW, some numbers. The rendezvous server that I run gets reports from clients about the success/failure of the key establishment phase. Over the last year, there were 85k sessions, of which 74% resulted in success, 22% in timeouts, and 2.5% in bad key-confirmation messages (meaning either a failed attack, or someone typoed the code). So in the worst case where every one of that last category was really a failed attack, there's roughly a 2130/2^16 = 3% chance that someone managed a single successful attack last year.
But I tried to make it easy to choose a different tradeoff. `alias wormhole-send=wormhole send --code-length=4` gets you to 2^-32 and gives codes like "4-absurd-almighty-aimless-amulet", which doesn't look too much harder to transcribe.
They just used your "secure" file transfer mechanism and their data got stolen.
You're on the same side of this as the airline industry. The person driving a car understands intellectually that their drowsy half-attention to the road is statistically going to kill them, whereas travelling in coach on a mid-range two engine jet liner is not - but emotionally they consider driving to be fine because they're doing it, and air travel is trusting some random stranger. As a result, the industry need to make air travel so ludicrously safe that even though emotionally it still feels dangerous the passengers will put that aside.
2^-16 is intellectually defensible, but my argument above is that shouldn't be what you're going for. So that's why I'd suggest a longer code by default.