Edit: it's so ancient that even I nearly forgot about them, but credit cards used to work by having the company take an impression of the card, then send in the receipts. sure, it might take a few days for transactions to complete, but it worked for several decades. there are fallbacks available to us, if we would just decide to allow for it rather than just failing
As with most decisions this one is a series of tradeoffs. Appreciate the reminisce and the fun metaphor though!
We all started with POP email accounts, but even way back then, that was tedious if you used multiple computers. IMAP was the trail blazing cloud app before cloud was a thing. Also, I would absolutely not want all of that crap from the SPAM folders local to my device taking up space, potentially malicious to my device, or any of the myriad other reasons why email doesn't need to be local to my device.
Imagine you're a product manager at McDonald's. For the point-of-sale kiosks, you can build the server component for deployment in the cloud, or you can build it for on-prem and add the overhead of physical deployments across tens of thousands of retail locations, plus maintaining them, plus dealing with franchisees.
You do a cost-benefit analysis of potential downtime from internet outages, and based on internet reliability numbers in the markets you serve (plus an uptime estimate from your devops org), you conclude the occasional outage is worth the trade-off.