This is something I've never quite got my head around. How do people think these third parties are storing their coins? On an airgapped machine or hardware wallet? Maybe. Hopefully. I'm sure many just use plain old software hot wallets though. What's the thought process here? "I don't trust my own software wallet, so I'll store my coins in someone else's software wallet instead, and hope they continue to allow me to access them?" Makes no sense.

If you aren't confident in storing coins yourself, the correct next step is to learn how to remedy that problem, and not assume even larger risks by giving away complete control to someone else.

In this hypothetical scenario of carrying bitcoin across a border, I would also prefer to carry an encrypted wallet in some form on my person. Indeed, I have done just that several times without any issues whatsoever. If, however, I was unduly concerned about being searched and it being found because I was Edward Snowden or something, then storing it encrypted online isn't necessarily dangerous. Provided I used a secure encryption algorithm and a long and random encryption key, then I could quite safely store it online, especially if it is only going to be for a short period of time (say, the 12-24 hours needed to take a flight, get through the border, retrieve the data, and sweep the bitcoin to a new wallet).

The caveat to this is the long and random encryption key. To be as secure as a 24 word phrase, you would need 39 random characters drawn from the full ASCII set. Are you going to write that down and carry that across the border? Are you going to try to remember that? I would argue that remembering 24 random words is easier than 39 random characters. As stupid as relying on your memory as a back up is, this might be a case where remembering your seed phrase is the least risky option.