In what sense is the question asked? Deep, in what way(s)? Most prolific writer? How many not only of his time, but since, have written more than Tillinghast, who's golf writings span over forty years? Is it the breadth of golf topics? Again, Tilly wrote & commented on courses, holes, ideas for holes, bunkers & hazards of all types, grass, trees, greens, green entrances, poetry, competitions & championships, gossip, etc... the list is nearly endless.
Unknown to but a few, Tilly started giving lessons after the debacle over his amateur status in the teens. Among those who visited his home in New Jersey for talk & swing analysis in the 30's were Bobby Lones & Ben Hogan. In fact, he made a movie of Hogan's swing that the two of them spent time analyzing frame-by-frame.
Is "deep" asked then in the sense of topics non-golf related as well? Tilly wrote about social issues and politics, as well as being greatly interested in the theatre & shows, classical music, motion pictures, etc... For about a ten year period, from about 1912-22, he & Lillian used to have students from Penn University visit his home on Saturday evenings for lively discussion & debates on the issues of the day - in fact one of them, Philip Brown, married his daughter.
Though I'm not sure that Tilly was the deepest of all the golf giants of his time, certainly no one was MORE prolific in range, volume or opinions than he.