Is nonce-less Encrypt-then-HMAC as secure as poly1305
Even though they have slightly different properties, both Poly1305 and HMAC take a key and a message, and return an authenticator. A nonce is not a parameter they have.
The nonce is a parameter of the encryption and decryption functions. For a given key, different nonces are likely to generate different ciphertexts. And in an encrypt-then-MAC construction, different ciphertexts are consequently likely to produce different authenticators.
So, using a HMAC doesn’t prevent usage of a nonce. The nonce is not used by the MAC function itself, especially in an encrypt-then-MAC construction.
It also means that a static (or reused) nonce can be catastrophic no matter what MAC is being used.