According to orthodox Theravāda, its on coming to nibbāna there is a cessation. Its not that nibbāna is cessation itself. If Ledi Sayadaw and Mahasi Sayadaw say different, then they are simply propounding their own personal views. The commentaries etc are quite clear. Nibbāna is not a cessation. Its a real existent, but beyond all concepts. Ācariya Anuruddha positively denies what you are claiming
Moreover, because it has been called “escape” by the Blessed One. For “escape” is a name for Nibbāna. As he said: “There are, bhikkhus, these three things that are difficult to penetrate. What three things are difficult to penetrate? These three elements of escape. This is the escape from sensual pleasures, namely, renunciation. This is the escape from forms, namely, the formless. Whatever is existent, conditioned, dependently arisen, its cessation is the escape from it.” Thus it has been said. If this Nibbāna, spoken of thus, were to reach the fault of non-existence, then the first jhāna and the base of infinite space would also be non-existent. Therefore, it is improper for the indestructible Nibbāna to incur the fault of destruction. Thus, destruction is not Nibbāna.
What you are arguing for was the Sautrāntika view.