The article doesn't discuss this; what are the advantages to using Let's Encrypt for internal services over deploying internally signed certificates? Are there any disadvantages to using Let's Encrypt?

The rate limits alone seem to be a potential danger if they need to reissue new certificates for their 65,000 servers.

The disadvantages are:

it’s less secure — you’re trusting (many) third parties with your security and relying on the security of DNS

it’s less flexible — you can’t sign certificates with internal names (e.g., *.cluster.local) and certs must be for 90 days, etc

it’s kind of hacky — you have to work around rate limits and whatnot because Let’s Encrypt wasn’t designed for this use case

The advantage is it’s easier. But that’s arguable. What the article describes isn’t easy. Using something like cfssl (https://github.com/cloudflare/cfssl) or vault (https://github.com/hashicorp/vault) or step certificates (https://github.com/smallstep/certificates) (which I work on) is probably easier and definitely better for internal services.