I think the last time I issued non-wildcard SSL certs for my domains was when I was still making the mistake of self-hosting email and the entire setup was a rickety mess.
Personally, the way I'd solve the problem in the situation where it'd be a problem is to not put auth on the same domain; auth would go to auth.secondexample.com. That's generally speaking the better choice to begin with due to browser weirdness regarding domain isolation (which is also why you often see software with CDNs use completely different domain names; reddit images being hosted on redd.it for example but also YouTube thumbnails being on ytimg. If they didn't, a maliciously formed file could read out browser storage for different subdomains).
Nope: one can setup ACLs so that the script that can update the records for printer.lan… cannot also do foo.lan… or any *.lan….
Poor security practice to use a wildcard. I completely agree there. But I can understand how wildcard certs work well for the average Joe who just wants internal stuff to be served over TLS without having to think about it too hard.
I work in security, so in my view, having the most secure internal network possible (think ZTA) is certainly up there.
Although I have come up with an alternative approach to achieve this.
This will allow internal-only services to get LE/ACME certs, but those cert will still show up in the CT logs and be visible to the entire world.
Some folks do not want that visibility, and that's what an internal-only CA gets you.