Honestly banning cash would be one of the easier things to do, but I don't think what you've said is necessarily true.
I cannot offer legal advice here, but my understanding is if Bob in NY has the fantastically idiotic idea to send $100k through the mail to cousin Suzy in CA, he wouldn't be violating in laws by not filling out the 105 or IRS 8300. He's not engaging in a trade/business and the money is not leaving the borders.
I meant internationally, domestic cash transactions don't currently have reporting requirements per se. Most domestic cash mails would eventually reach a magnitude large enough to meet a reporting requirement for sales tax, 1099-MISC, gift tax, etc.
I cannot offer legal advice here, but my understanding is if Bob in NY has the fantastically idiotic idea to send $100k through the mail to cousin Suzy in CA, he wouldn't be violating in laws by not filling out the 105 or IRS 8300. He's not engaging in a trade/business and the money is not leaving the borders.