Is the non-responsiveness to supplication due to not invoking blessings upon the Prophet (peace be upon him) a general ruling that includes supplication during prostration?

In Islamic law, supplication (du'a) is divided into two categories: absolute and restricted. For absolute supplications, such as praying in the last third of the night and on the Day of Arafah, it is recommended to invoke blessings upon the Prophet after glorifying and praising Allah. There are reported gradations for invoking blessings upon him: before, during, and after the supplication. As for restricted supplications, such as the du'a for entering and exiting the lavatory, the du'a for strong winds, the du'a of Istikhara (guidance), and the du'a in prostration, blessings upon the Prophet are not added to them. This is because the Prophet (peace be upon him) did not teach us to add them to the text of these specific supplications. One should suffice with what is mentioned in the original text of the supplication. An exception to this is the supplication upon entering the mosque and after the adhan (definition), as invoking blessings upon the Prophet (peace be upon him) has been reported for these two instances.