To complete our look at potential Hall of Famers from the 1920s, we have the bottom tier. These men were very good players indeed, but although some of them were honoured with inducted, it's difficult to make a case for them based on the results of their careers.
At the top of the list is Jack Adams, who was a very effective centre in his prime, but didn't have enough good years to really be considered an elite player. Surely his lengthy tenure as GM and coach of the Red Wings did nothing to colour the memories of his abilities as a player.
Ace Bailey's induction is a tragic one, in the sense that he was inducted due to a tragedy. Bailey had one outstanding season in 1928/29, but other than that was good-not-great. His injury probably didn't prevent his meritoriousness, since his offensive production had already dropped considerable before Eddie Shore's hit.
Billy Burch was more famous than his ability suggests he should have been. He rep was embiggened by promoters when the Hamilton Tigers moved to New York, being called the Babe Ruth of Hockey in an effort to draw fans to the games. He was very good, but did not deserve the Hart Trophy he won in 1925, and has not real claim on a spot in the Hall of Fame. Burch's linemate Wilf Green is an even worse selection; he barely even beats out his brother Red in terms of meritoriousness, but his fame as the leader of the Hamilton players strike created name recognition that his play could not.
That leaves us with Phat Wilson, Harry Watson and Moose Goheen. These three are similar in the sense that none of them played at the highest level of the game; only Goheen even played professionally, in the minor leagues from 26/27 to 31/32. They all benefit from this fact, because they never had to play against the very best competition available. Memories of their play can therefore easily be overestimated. Although I'm missing much of Goheen's early career, the numbers we do have don't suggest Hall-of-Fame calibre. Neither do Wilson's; he was the best player in a fairly weak league (Thunder Bay senior league), which grew even weaker when the minor professional leagues become organized in 1926/27.
Harry Watson is a bit different. Although surely inducted for his performance in the 1924 Olympics, Watson was in fact an excellent player, one who could have most likely had a very good NHL career should he have chosen that route. He effectively retired from hockey at age 26, as so many amateur players did, playing only a game or two per season after that. If he had a full-length professional career, he'd be much closer to the "maybe yes" line here, although he lacked the (at least) one really big season most Hall-of-Famers have.