X25519 is an elliptic curve Diffie-Hellman function and doesn't take a nonce. If you're asking about ChaCha20... yes, which is why nonce reuse misuse resistance is an important theme of CAESAR.
Sorry, don't know why I wrote that, I was thinking ChaCha20/Poly1305. OP picks on all the other AEAD modes for failing with nonce reuse, but doesn't mention it's actually the same failure mode with ChaCha20/Poly1305.