I just like to comment on the verse you mentioned i.e.,
This is not an imperative statement but a fact is described that no one can even touch the quran except the pure ones. No one except those who are ‘pure’ in true sense of the meaning can get to the gist of Quran. that is why it is called ‘guidance to the righteous’.
So being physically clean before touching Quran can be a derivative of this Quranic verse since physical cleanliness plays an important role in becoming spiritually pure