This might be a reasonable solution if it's a one-off unique solution and is therefore unlikely to be detected. But if you can't count on security through obscurity, this is a good way to end up serving real jail time.

However, it's pretty well understood criminals aren't legally required to self-incriminate. For example, if a criminal was to hand over their password, they're not then obligated to assist border security in navigating through their phone's storage to specifically point out evidence against themselves.

Whilst I'm not advocating this solution for criminals(!), I'd assume the same logic ought to hold true for those that have careers where privacy is paramount.

If you simply boot up your phone (into the "non-private" environment) and have no password, or perhaps even use the same real password (remember to change it later), then it's not necessarily your fault the border agents don't know how to use your phone.

EDIT: In terms of lying / being discovered, this is why I'm proposing a low-level dual-booting solution, rather than simply having multiple profiles on the device. It ought to be 100% undetectable that the device supports dual-booting at all, unless the user performs a precise action to boot into the private environment e.g. connect the phone to PC, and submit a specific boot command with a user provided password. Without the correct password being provided, the phone should respond no differently than a phone that does not support dual booting.

Although, IANAL nor have I made any attempt to look into the laws surrounding this. I would be surprised, although not too surprised, to hear there are laws specifically covering this situation. Nonetheless, it'd be a loophole for sure, and presumably easy enough to close off with further legislation.

Also, does anything like this exist for desktop operating systems?

For example, I believe Truecrypt has a dual container system with two passwords in addition to their regular encrypted containers. You enter one password to get to the "fake" container and another password to get to the "hidden" container. Plausible deniability exists where it is impossible to prove whether you are providing the hidden password and whether there is a second hidden container.

Could a similar system be employed for a mobile device? The core OS components could be shared by both containers and it's clear that you could potentially have a second hidden profile, but it's not possible to prove that it exists.

Of course just the presence of countermeasures on your devices would raise suspicion.

If you're at the point where this seems like a good idea, you're better off not bringing data over the border.