Even failing to renew a corporate franchise with a state "only" has the consequence of that corporate entity being administratively dissolved. While likely catastrophic for that specific corporation, if "Example Widgets Ltd." fails to be renewed, I can't come along and register "Example Widgets Ltd." on the corporate register and then ring up the bank of the former Example Widgets and say "hi there it's me Example Widgets please hand over checking account."
All of that said, I don't know if there's a better way to handle this. If we assume that domain names must expire--which we currently do, and I can make an argument for and against that assumption--then what's next? It's expired but never usable again?
Good thought experiment for the morning to take my mind off of COVID's impacts on transit funding.
It's still pretty ridiculous, because businesses have plenty of other periodic filings and fees and renewals to deal with that have nothing to do with computers. There are permits that need renewal. Old fire extinguishers need to be replaced or recharged to avoid fines when the fire inspectors come around. There are all kinds of tax filings due monthly, quarterly, and yearly. There are various trademark and patent maintenance fees they need to pay during the life of a trademark or patent to keep it alive. They might also have long term contracts with janitorial services, landscaping services, copier/fax maintenance services, utilities, payment processors, and many others that they might want to review a couple weeks or months before they expire to research if they want to change providers.
Somewhere they should have a shared unified calendar of all these things, listing when they are due and what manager in in charge of getting them done. The computer stuff, like domain renewals and certificate renewals, should be on there.
This calendar should be regularly checked by someone high up, like the COO. That person just has to check it enough to be aware of any deadlines approaching, and if they do not get marked as "in progress" as they get close this person can poke the head of the appropriate department to get it taken care of.
Sure, a department could still have forgotten in the way you describe, but it gets noticed before the deadline giving them time to figure out how to fix it. But unless you get a chaotic shake up at the top, it should be nearly impossible for a company to actually forget about any of the aforementioned deadlines.