As you will appreciate, US immigration regulation and operations are a matter solely for the relevant US authorities, and the Department of Foreign Affairs is not in a position to intervene in decisions taken in relation to ESTA applications.
However, officials from my Department regularly engage with the US Embassy to discuss immigration and visa matters in general terms. I understand that ineligibility for an ESTA does not automatically make an individual ineligible for a US visa, and that any applicant who is denied an ESTA may apply for a visa through the US Embassy. My Department’s travel advice to Irish citizens planning to visit Cuba includes information on the potential impact on ESTA eligibility. This advice can be accessed at www.dfa.ie/travel/travel-advice/a-z-list-of-countries/cuba/. Information on current visa appointment wait times at the US Embassy can be found at travel.state.gov/content/travel/en/us-visas/visa-information-resources/wait-times.html.