I would expect Jayson to achieve hall of fame.
I'm no expert on the HOF. I don't know how many people they induct, how many they exclude, what the requirements are, etc.
If it was up to me, though, I wouldn't go strictly on number of #1 finishes in international events. I'd also consider other factors such as place on the money list (giving credit for consistent deep runs), peak Fargorate, known ability/notoriety, high straight pool record, and of course career longevity once it's gone on a bit longer. Adding this all up it seems to me he belongs.
If the HOF is strictly off of international titles and they have clear standards he fails then that's up to them, but that would just make the HOF lose credibility with me personally as it wouldn't reflect the total of a player's greatness.
PS- He has also won the US Open. I was there in 2017 when he looked invinsible against Klenti Kaci in the finals and FSR in the hotseat match. When Shaw is on a roll it is something special!