Do the supererogatory Sunnah prayers fulfill the purpose of making up for missed obligatory prayers?

Scholars have unanimously agreed on the obligation to make up missed prayers due to an excuse, such as sleep or forgetfulness. The majority of scholars are of the opinion that it is obligatory to make up prayers deliberately missed, and that an abundance of supererogatory prayers does not suffice for them. This is the view of the Four Imams. Whereas some scholars are of the opinion that making them up is not obligatory, because making up a prayer must be commanded by the Lawgiver, and His command is specific to those who missed the prayer due to an excuse. The view that making up the prayer is obligatory is the most preponderant, the most cautious, and the one that best absolves one's responsibility, and supererogatory prayers do not suffice for it.