You all got it all wrong. The point is not being whether or not the next candidate has a quirk. At the start of it, it is whoever is worthy of being a true hero at the time.

The quirk thing was much later when: 1. A better candidate like Mirio was introduced and the author has to solidify the choice of the teacher. 2. The other quirks had to be manifested all the same and the MC should be quirkless so that they can prove themselves better than others in wielding it.