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.