Is it contrary to the Sunnah for the mosque supervisor to assign a reciter for each prayer, working towards the completion of the Quran starting from Surat Al-Baqarah, and specifying a daily portion for each student and a particular day for each reciter?

There is no objection to having a different Imam for each prayer, and there is no objection to reciting the Quran according to the order of the Mushaf. Al-Bahuti mentioned that Ahmad ibn Hanbal permitted recitation according to the arrangement in prayer, and Al-Nawawi stated that it is preferable to recite the Quran according to the order of the Mushaf, whether in prayer or outside of it, because the arrangement of the Mushaf is for a wise purpose.