Sometimes you don't want to make that information public though. For security (you don't want to publish your whole tech stack information) and secrecy (you don't want to publish registration of halflife3.internal.valve.com).

Then just use a wildcard cert.

Wildcard certs are a security ops nightmare. You really don't want to throw the private key for that around to every small project, and you need some good, automated way of rolling them across multiple services. Doable, but if you can avoid this, it's a better to avoid.

This 100x - in just about any organisation of any size, if you use a single wildcard cert for all internal services, then it's inevitable that the private key will end up in the hands of an employee that shouldn't have it.

I'm aware you can use Lets Encrypt that way, I just don't agree that it's bad use of an internal PKI to use it as an alternative.

Well, it's unnecessary work to install and maintain that internal CA. Keeping CA key safe is very important, because leaked key might lead to your internal connections to, e.g., Google be compromised, so it's like keeping a bomb inside your building. If you already have that internal PKI, you can use it, sure, but I still think that it's a bad idea to use it only for internal websites.