Edit: this does not appear to be a thing that happens.
As for the rest, chalk it up to my over-active imagination, compounded with that bad knowledge. SSL is an SEO boost (according to a random Googling), and if domain name expiration was a factor, it made sense to me that SSL expiry would factor too.
TLDR, I was a dumb.
It's even worse than that:
A smart attacker will copy the method used to generate keys, and leave the server. Then they can keep generating keys and you will probably never notice.
I feel that automation is a mistake, something security sensitive like this should be on a completely different machine.
It would be trivial to move this to a separate machine by using a reverse proxy for .well-known instead of serving it directly from your load balancer's filesystem. The rest is just scp'ing your certificates and keys to your load balancers (or using your configuration management software of choice to achieve the same). With ACME being an open protocol it's quite likely that someone will end up writing a client specifically for this use-case, making it even easier.