Anas ibn Mālik (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) did not say the Qunūt but he would pray for welfare of a people or doom of others.
This noble Hadīth shows the cases in which the Prophet (may Allah's peace and blessings be upon him) used to say the Qunūt. He used to do it either when making supplication for some people or make supplication against some people. This confirms the permissibility of saying the Qunūt during disasters or calamities. There is no text proving that Qunūt has been made in obligatory prayers except at times of disasters and calamities. This is because the Prophet (may Allah's peace and blessings be upon him) did not say the Qunūt except he would supplicate for welfare of a Muslim people or supplicate for destruction of the disbelievers. This type of Qunūt is not specific for a certain prayer; rather, one should do it during all the prayers.