To be honest, just because you can (legally), doesn't mean you should (do it). Carrying cash in the US is dangerous, and not just because of regular street thugs.
They do not need to prove anything to seize your money. Stealing from people carrying too much cash on them has become a national past time of the police in the US. There are police departments that rely on this to provide them with funding :
> In some Texas counties, forfeitures fund nearly 40% of police budgets.53 The Cook County, Illinois state’s attorney’s office’s 2016 budget anticipated $4.96 million in forfeiture revenues, which it earmarked to pay forty-one full-time employees’ salaries and benefits.54 But forfeiture proceeds are not just used for policing activities; with little accountability, law enforcement officials have also spent them on extravagancies like expensive dinners, parties, and personal expenses.55
> As a result, the decision to pursue a forfeiture is often governed not by justice, but by “department wish lists.”56 Police civil forfeiture trainings include instruction on “maximizing profits, defeating the objections of so-called ‘innocent owners’ . . . , and keeping the proceeds in the hands of law enforcment.
> And over time, across all 50 states and the federal government, those small sums add up: between 2000 and 2019, according to IJ’s calculations, authorities seized roughly $69 billion from people, most of whom were not even charged with a crime.
All it takes is "mmh, this guy has suspicious cash, and we need some funding, let's steal it and say it must have come from drug deals, while not actually charging the owner with any crime".
Offtopic: I'm baffled that this kind of open robbery is completely legal and there's. Practically nothing that can be done to recover your money. This among other crazy "normal" things in US make me extremely wary of even visiting.
https://www.cbp.gov/travel/international-visitors/kbyg/money
But I agree with the general principal that this should be inflation indexed.