Dr. Sax was no city shroud
In fact I think Kerouac wrote Dr. Sax in Mexico not long after writing On the Road in New York. I think it can be seen as a kind of flip side to On the Road, Kerouac's unconscious getting back in touch with all his old Lowell childhood memories and with all the ghosts haunting the American continent that he had encountered on the road.
Dr. Sax is a great work of literary art. If Kerouac had been European--think Joyce, Hesse--he would have won a Nobel Prize for this one.