Kelly Mae at TSA also wrote:
The issue with the cash is, "if found", it is a scenario for further scrutiny in which the LEOs may get involved, especially if you are traveling out of country with said cash. (that IS illegal) There will be some questioning involved, but it's only to ensure it's not illegal, and if all is kosher, you'll be on your way.
I have repeatedly asked her whether she thinks this sort of behavior is constitutional, but she has not answered.