> Is this a problem for Let's Encrypt? Doesn't Let's Encrypt's verification require creating files with random names in http://example.com/.well-known/acme-challenge where example.com is the certificate's common name?

That applies to the http-01 challenge. The tls-sni-01 challenge works solely based on the returned certificate. If the SAN value in the certificate matches the SNI value sent by the validation server, the challenge succeeds.

Would you mind sharing which control panel you tested this with?