I believe above 10k, you're just required to have a source for the 10k. One of my buddies in college brought his entire school tuition in a suitcase over when he started school and it caused a bit of a shit show because he had to go back home and get proof to release the money or something like that. He came from a wealthy family so he had never ran into that before.

You can't leave the US carrying more than $5 in nickels and pennies though.

https://moneyweek.com/33401/why-its-now-illegal-to-melt-down...

https://www.federalregister.gov/documents/2007/04/16/E7-7088...

From one of your links:

> The United States Mint nevertheless acknowledges the concerns raised by the commenters. Therefore, the exception provided for in the current regulation at section 82.2(a)(2) has been amended to reasonably accommodate these concerns by allowing exportation of 5-cent and one-cent coins having an aggregate face value of up to $25 when it is clear that the purpose for exporting such coins is for legitimate personal numismatic, amusement, or recreational use.

It's still a weirdly low limit.