The issue might be executing 3rd party code on a server.
I want to go to a website, have it tell me to put a string into a meta tag or DNS TXT record, and then save the key it returns on my box. Then I want to forget about it for the next 2-3 years.
Honestly I don't even want to do that. I want my nameserver to generate a DANE/DNSSEC record for me automatically, and for browsers to honor that. It isn't like domain verification is any more secure than a DNSSEC record would be.
We do something similar, although not through a REST API. We handle all this cert management centralized on one server, which publishes the DNS records for DNS verification etc.
On our other servers is then just a simple script that periodically checks if the certs on the machine are near the expiry date and if so pulls a new one from the central system.
With many commercial registrar's, although they offer a valid and long certificate, their technical aspects aren't very good. Many CAs don't support ECC certificates, the must-staple flag or CT SCTs embedded in the certificate.
I work a lot with web PKI, and every time I have to deal with a CA that's not LE or Digicert, I sigh out loud.