I know this doesn't address your comment head-on (i.e lost password) - but it does address the issue of stolen phones which are apparently impossible to restore back to their factory settings.
Most people who rob iPhones are not technically savvy, but they know people who are, and they get those people to debrick the phones.
The real question is: who are these people who can unbrick iPhones?. Well it turns out: all you need to do is look on your town noticeboard and there are a slew of people who claim to 'unlock' or otherwise debrick iPhones.
Typically the tech they use to debrick the phones is readily available on the web, and god knows what other things they do to the phones once they are 'market ready' and ready to be sold (malware implants, either accidental or deliberate can be found on these devices).
I know from experience and know a few people in those circles who deal with stolen phones all day, everyday. There are also firms who demand proof-of-ID so that stolen phones can be tracked and tied back to an individual. The firms that don't require ID have something to hide (they typically ask for no ID and happily sell you a stolen phone for a cut price).
Q: What's your password?
A: I have no idea.
Q: How do you log into computers then?
A: I'm going to invoke my right to remain silent now, thanks.
[I am under no illusion that this actually helps the compelled decryption situation]
Of course you cannot take back what escaped your mouth prior to asserting for right to remain silent.
It's also useful to be able to leave the physical key at home, or with another party.
... and if you hand it to your attorney, does that count as privileged communication?
I use my password manager to save things that are not passwords too- padlock combos, combo to my safe, medical info, parents wills, banking, all my dirty secrets... Seems wrong they could get access to all my info if the warrant is just for Xyz.
It doesn't really matter if the process fails, it would just be nice to regain access, and it would be interesting to learn how to do it.
Does it boot on its own, without entering a password?
I'm on the wrong side of the ocean, alas, but I'm betting this won't be too hard to crack.
It does have FDE, and requires a password on boot for that.
If so, just take the disk out and plop it in another machine and-- you're done.
If not, then no cold-boot attack can possibly work.
You know that, I suppose. You'll have to crack it by using FireWire or a similar method that lets you read/alter memory, or by opening it up and connecting probes directly to main memory. I have no problem telling you that the latter would be harder.
I certainly would not be able to do either.
This tool could help you, possibly.