You’ve described a few mechanisms that are different than sending cash in an envelope: check, money order, ACH, wire transfer.
I guess all of these too could theoretically be replaced with crypto depending on your need and situation. With something like a wire you are placing the transfer in the trust of your bank, which is secure but can take multiple days and can cost more than an ETH transaction.
Most mail arrives fine but mail theft is still a massive problem and rising, it is one reason you are advised not to regularly send cash in the mail.
That link is almost entirely about package theft, not ordinary letters. Even if I accept the figure of 3%, that's equivalent to a $3 insurance premium on sending $100 cash, not too bad. I'd put it at way under 1%. Lots of us still pay our rent and bills every month by mailing checks, same with annual tax returns etc., and losses in the mail are rare even though those sorts of mailings are identifiable as being likely to contain payments. A hand addressed envelope to a random person is less likely a priori.
Domestic wire transfers are almost instant, while international ones can take overnight.
Doing anonymous and untracked payments of significant amounts at scale is sure to tick off regulators. If your ETH transactions are non-anonymous and tracked, it's hard to see any superiority over ACH or wires. It's a solution looking for a problem.
I don't regularly send cash in the mail but I've done it a number of times, with no losses that I know of. A typical reason is that I don't feel like going to the hassle of getting a money order. I feel like sending a personal check is riskier than sending cash, since a stolen check reveals my account number, leading to possibly unbounded loss. I generally do use money orders if I might need proof of payment afterwards, or if the amount is high enough to worry about. I've sent $100 cash on a couple of occasions but more typically it's $10 or $20. Even that is an occasional rather than a frequent thing.
If you are sending cash numerous times in the mail I would say this is a problem and technical solutions that aim to improve on this are beneficial. That said, you and the receiving party may be living in more fortunate conditions. Many people in the world live in apartments, with mail rooms that are not well secured and are frequent targets of package theft.
Domestic wires are slow in many countries, in the order of days, and costly[1]. My ETH transactions are done in 30sec, fees are usually less than a dollar, and they are pseudonymous - primarily only known to my CEX and government. The transaction is traceable while in transit and proof of payment easily found.
To me, it sounds like you are writing off ETH transfers without having actually used them.
Why do you want a CEX and the government to have their hands in your transactipn? Does the recipient also have to deal with a CEX? If yes, that is another hurdle. And why do you keep referring to package theft when the cash is sent in an envelope and not in a package? Packages get stolen because they have stuff inside. Envelopes that look like random personal correspondence is much less attractive. If you have any stats about mail theft that is about envelopes, I'd like to see them, but stats about packages are something different imho.
Fwiw, I live in an apartment, and any letters are delivered to my mailbox, which has a lock. There is not much likelihood of letters getting stolen after delivery. Packages that don't fit in the mailboxes are left on top of the mailbox, and those are much more exposed to getting stolen.
Yeah I'm not speaking for other countries, not all of which have functioning payment systems. ETH (current version) does sound more efficient than BTC.
I guess all of these too could theoretically be replaced with crypto depending on your need and situation. With something like a wire you are placing the transfer in the trust of your bank, which is secure but can take multiple days and can cost more than an ETH transaction.
Most mail arrives fine but mail theft is still a massive problem and rising, it is one reason you are advised not to regularly send cash in the mail.
https://safeatlast.co/blog/mail-theft-statistics/#gref