Dr. Barton Explains why Leonardo didn't paint the Grail

One of my students, taking an argument from one of Dr. Langdon's books, asked me 'Why didn't Da Vinci paint the Holy Grail in his Last Supper. I answered him:

Firstly, his name was Leonardo. Calling him Da Vinci is just wrong.
Secondly, the Holy Grail legend had very much had its day by the Renaissance. It was never that popular in Italy anyhow. The best Grail romances come from France.
Thirdly, the Last Supper was painted in a monastic refectory, and the Church disliked the Grail legends, never conferring any approval on them.
Fourthly, expecting to find the Holy Grail in Leonardo's painting is our projecting a modern view on to a Renaissance source. Until the revival of interest in the Arturian romances in the Romantic period, the Grail was all but forgotten.
So, I concluded, it was really unreasonable to expect to find the Holy Grail in Leonardo's The Last Supper. My student agreed with me.