Because 'funny man' bill will constantly be distracting sean with his endless series of one-liners and other inanities. Mostly walking should be reserved for children's adventure games (Nancy drew worked pretty well, as did older, sillier adventure games), while Sean can play games that actually require serious thought and a more serious approach on Fridays. He's the only one I trust to solve puzzles since he's a bonafide mathematician :).
Can you imagine Bill interjecting every minute while Sean played the Talos principle? It would have been terribly distracting and not very enriching.