Digital processors are not needed for "basic agricultural computations" nor for communication. A ham radio can work and transmit/receive information without any

Digital processors are not needed for "basic agricultural computations" nor for communication. A ham radio can work and transmit/receive information without any typewriter-like automation (both microphones and manual Morse code don't require computation) and you can do all the calculations needed for ordinary agriculture on an abacus if needed. In any case, the extremely precise machining in large quantities required for any reasonable mechanical computer means that it's not a low-tech or high-reliability replacement for electronic computers, it's a very high-tech future solution to the limitations of current electronic devices. We can't make such devices now, we'll hopefully be barely able to make them in the future, but in the case of infrastructure collapse we'll lose the capability to make these advanced mechanical devices before losing digital devices. And nowadays computing is so ubiquitous, that every horrible scenario would still leave us with huge amounts of computing power lying around. Soldering together devices out of scrap electronic components is a much more reasonable way of doing post-apocalyptic computation than any of this mechanical computing tech; If there was a real need, nowadays you could extract a dozen usable processors from a crashed car or modern kitchen - even excluding computers and smartphones, so many modern devices have random processor(s) that are more powerful than what people used as their primary computers some decades ago. Things like wireless headphones and washing machines have chips that could be sufficient for so many computing needs. Apple's Lightning to HDMI cable has a powerful ARM processor inside. etc, etc.