Unless Apple already inserted a secret backdoor that allows for forced updates, you don't have to update the phone when it prompts you. The closest I've seen it get is a reminder that asks you if you'd like to schedule an update for 2:00 AM or some such time, and then asks for your passcode to do so. You still need to type it for the explicit purpose of updating for it to go through.
I know that recent updates download automatically on Wi-Fi, perhaps that was what you're thinking of?
The 5th protects you from being compelled to be a witness at your own trial, it does not however protects from destroying evidence, interfering with a police investigation or hindering justice.
If you intentionally destroy incriminating evidence that's a crime, if you prevent the police from executing a search warrant that's a crime too, a court can order you to present existing physical evidence including private diaries, recordings, or anything else and refusal to do so is a crime.
Now while you can say that a code is "speech" it's wouldn't be that hard to claim that it isn't, handing out a code isn't baring witness, this isn't speech in any sense, you can already be compelled to give DNA and fingerprints.
That code essentially is a device that serves only 1 purpose and it is to unlock your phone, if you build your house in a nuclear silo and refuse to give the police the keys when presented with a search warrant they'll lock you up, quite a few constitutional lawyers can argue that this example can also be applied to passwords, encryption keys, and other similar devices.
Whether it's a crime for the device owner is an entirely separate question; there's case law in both directions about whether you can be compelled to supply the passphrase or unlock the device. (That case law also varies by jurisdiction.)
There's an entirely separate question about whether the device vendor can be compelled to introduce a backdoor where none previously existed. And you could quite reasonably argue that even if the device owner could be compelled to unlock the device, the device vendor should not be compelled to produce a less secure device, any more than a safe manufacturer should be compelled to produce a backdoor combination that unlocks one of their safes.
And if you have the key to your nuclear silo in your hand but refuse to unlock the door, the police don't have to lock you up because they can take the key from you instead. But if the lock is a keypad then the scenario is identical to the iPhone and you're just assuming the conclusion. Your argument seems to distill into the idea that if the police can't read your iPhone without violating your constitutional rights then your constitutional rights have to give way.
This isn't the same situation that Apple has; while I bet the motions would be filed under seal, I don't believe it would create significant liability for Apple to have a warrant canary, and then remove it after the canary 'dies'.
In fact, in 2014, Apple's canary did 'die', with no further comment, and no public disclosure that their were material difficulties with the canary. Apple seems to have been working to enhance security on their devices since then. I would take from this that they didn't receive giant, secret penalties from their canary.
I thought you were saying EFF's assumption that a court cannot compel a canary to be maintained, would also prevent a court from compelling a software update targeting a certain user. Anyway, I believe we can't trust either a canary or software, because either can probably be compelled.
[0] https://www.washingtonpost.com/posteverything/wp/2014/09/23/...