I am sorry to hear about the damage done to your business. I appreciate that you took the time to list out those grievances. I'd like to respond on a few points, for the sake of clarity (if you're interested, but also for other readers here).
That header thing was indeed a bit of a fiasco; a misguided attempt to honour the few that stepped up to support Caddy monetarily. Once the depth of the issue was made clear to the developers, it was indeed walked back.
Regarding OS packaging teams - it's not the dev's responsibility to become approved package maintainers for individual distros; it's generally not done, either. The distro maintainers themselves decide which packages to make available, and how to package them. Caddy doesn't offer repos for the individual popular package managers because of the nature of Caddy's third party plugin architecture - none of the package managers allow arbitrary downloads from a build server (rightly so - the package maintaining process is intended to provide much higher assurance of security), and they don't allow for the package to be built to request either. Not only that, but those plugins may or may not be trusted by the user themselves; the usefulness of anyone being able to extend Caddy and publish their own plugin at any time comes with that downside.
The licensing arrangement was born out of a simple need - Caddy devs gotta eat. The code itself is Apache 2.0 - the Caddy project is as FOSS as it gets. The commercial part is the build server, which isn't open source - if you use it to build your binaries, those binaries are considered either commercial or personal in nature. I can tell you that the devs would like nothing more than to have a different method that would satisfy their monetary requirements so they could make the build server binaries free, too.
The idea behind exiting on start with an error is to ensure that when the user starts the server, they know straight away that there's a problem and Caddy can't do what you're asking it to (which is manage your HTTPS certificates). There are ways to get Caddy up, even with out a valid HTTPS certificate, and get your site online regardless - they're just not _automatic_.
The fragile state concept is one we come across frequently. The truth is that when people say they're restarting the server, the meaning of restart is "shut down, then start", instead of "reload". Caddy has graceful reload capabilities; you can swap the Caddyfile and even the binary itself out without interrupting the server (this isn't true on Windows, though, where varied signaling of the Caddy process is not possible in the same way as it is on *nix based systems).
I myself have posted working solutions to full live server migrations (for the entire set of websites), between two fully working and secured (HTTPS) Caddy instances, accounting for DNS propagation. It's not unsupported or difficult, just not _automatic_; it requires some specific configuration and a careful hand (like most live site migrations). The somewhat-recent filesystem clustering Caddy does isn't even related to migration - it's actually supportive of distributed fleets solving challenges for other instances. You've always been able to share the TLS assets between Caddy instances and have them be used.
I wish I (or the developers) had been given a chance to offer some guidance - I believe we would have been able to help avoid some of the downtime and losses suffered by your business.