The scenario is: you’ve managed to receive ₩500,000,000 (~$337,265) at a Korean lottery (the catch is, only given in cash) which is delivered to you in two duffel bags. However will there be issues when returning back to the USA with that amount of money since it’s bundles of cash via foreign currency when the cap is $10,000 for undeclared amounts?
This is true with all things in life, but with enough money, most problems fade away.
Banks will tend to drop most of those requirements in exchange for higher minimum balances and potentially fees. The amount of money you need for this will vary wildly country to country.