^reading as in learning environment is found in the ahadith whereas reading the Qur’aan in groups for khtam-e-Qur’aan, asala sawab etc isn’t. Please check these links for more info on this issue:
Ruling on gathering to make du’aa and recite Qur’aan
Reading Qur’aan together, giving good deeds to the dead
Here is the basic logic to understand these kinds of issues:
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Is it allowed to recite Qur’aan? Yes
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Is it allowed to do it in a specific manner at specific time at specific day for a specific purpose or with specific intention? If there’s an evidence then we do it, otherwise it is a bid’ah.
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By inventing new things or new ways to do certain acts of worship, you’re simply saying that Allah Ta’ala and His Rasoul (sal-allahu 'alayhi wa salam) left out few things or ways which could have benefited you in this world and here after, 'aoudbillah.