Postal mail and telephone were ... relatively secure, inasmuch as that bulk surveillance was expensive.
Wiredtapping and postal interception, as well as metadata (pen-trace and postal covers) are possible, but scale poorly when individual lines must be listened to by individual agents, or individual letters carefully opened and resealed.
Digital permits surveillance at mass scale. It seems ultimately a fundamental property of the medium, less a bug than simply a feature.
There is also a fairly robust tradition of privacy in postal mail (in most countries), and after some false starts, eventually applied to telephony, at least in theory. The situation for email is far less evolved.
These days, if you do want secure communications, postal probably offers some real benefits. I'm somewhat surprised that postal remailing services (send an outer message to a central point who deposits the enclosed prepaid inner envelope(s) to final destination(s)) isn't a thing, or at least not one that has any appreciable awareness.
The capabilities of voice-to-text and handwriting / optical character recognition make the viability of intercepting virtually any spoken conversation, or any _observed_ written communication, quite high. The costs are much greater than with straight machine-readable character text (ASCII/UTF-8/Unicode), but pretty tractable.
My view is increasingly that privacy is an emergent phenomenon responding to ever-increasing surveillance and observation capabilities. The modern discussion began in the 1890s (Warren & Brandeis: https://www.cs.cornell.edu/~shmat/courses/cs5436/warren-bran...), as technologically-mediated intrusions were increasing greatly in capability. Though what the end-game is I do not know.
I would argue that postal remailing exposes the remailer to legal risk, and (if done with few remailers) gives the surveillers few points of particularly interesting mail hubs.
If anything, postal remailing would probably only work in a TOR-like manner, with many, distributed, non-for-profit remailers - but that opens a whole set of new problems, like who pays for the service, what prevents the remailer to just take the delivery for themselves (as undoubtedly such a service would be used to remail illicit substances and other valuables), and how would such a network of legitimate, trustworthy remailers know each other to do some tunnelling?
There are numerous potential issues, yes, though some provisos (e.g., no detectable traces of illicit substances, limited to standard envelope-sized postage) would tend to limit much of that.
Even as an informal practice, the option could have some value. The question of whether to used a two-hop (source, mix, recepient) or three-hop (source, mix-1, mix-2, recipient, as with Tor) exists (the three hop system would triple postage, if messages were sent individually, though bulk distribution is another option, with break-bulk at the 1st or 2nd hop).
Again, what has surprised me previously is that I'd found no mention of the concept at all. Though I am finding several now, specifically emphasizing anonymity / location obscuring:
But a pidgeon leaves a trail of metadata on the ground as it carries your message, so this communication channel is still vulnerable to bulk network analysis by some Advanced Persistent Threat.
Telephone? Nope.
Ham radio? Nope.
Letters sent through the mail? Nope.