The people that are getting arrested are people that have never paid taxes or declared these assets/income.
I've carried well over $10,000 several times out of Argentina including a few months ago. I've never had any issues or problems.
But this money was all "white" and received when I sold assets in Argentina. (Car, apartment, etc). I was paying all taxes the entire time I owned these assets and also paid the correct taxes when I sold the assets (stamp taxes, transfer taxes, etc).
If I ever was stopped, I would have just showed the paperwork on this money. Keep in mind you DO have to legally declare any amounts over $10,000 US when you enter the USA. On the USA side as long as the funds are legal you can enter with it.
HOWEVER keep in mind that carrying over $10,000 and declaring it at customs is an almost red flag to get audited by the IRS. So it's not worth the hassle. I agree to just pay the 5%/6% to one of these reputable firms to wire it out.
I will say that it doesn't take up much room to carry up to around $80,000 US. A $10,000 "brick" of $100 bills doesn't take up much room. I never put it in a bag. I just carried it on me. You can have a good pair of socks and put 2 $10,000 bricks on each side of your socks on each leg. This is $40,000. Then you can fit another $10,000 in each of your pants pockets and if you have a long jacket to cover your pockets you wouldn't have problems. I've NEVER had problems with this or set off any metal detectors carrying this much cash.
But I have been audited 3 times in 6 years so keep that in mind. It's a major hassle to get audited by the IRS.