Shaw also gets credit for the world blackball championship and the straight pool record, not to mention his epic Mosconi Cup performances and his showmanship in the process. Without those he's not in the HOF.
From AtLarge's summary post of career Mosconi records, Shaw's is (10 yrs. -- 2016-2025) ..... 17-6 s, 16-11 d, 8-6 t, 41-23 total A (64%), 26.6-12.7 total B (68%).
Blackball is not pool, so that should not factor into his HOF resume IMO. Neither should a straight pool record that no top pro was trying to break other than him. It's impressive that he ran the 700 balls or whatever it was, but let's be honest here: if tomorrow some big sponsor announced a million dollar prize for the first person to break Shaw's record, it would be broken.
Similarly, Mosconi cup is an exhibition. It should not carry any weight in HOF consideration. Especially considering that it's essentially a no-contest most years.
I think Shaw is an interesting borderline case for the HOF. There's no doubt that when he's in top form, he's almost in a league of his own -- only Earl I would say has ever made the game look quite as effortless as Shaw did in his final match to win the International Open against Lechner, for example. But the problem is that that's Shaws' A-game. His average game is not nearly that elite, and his tournament resume is not even close to someone like FSR. I could go either way on whether he deserves a HOF spot, but ultimately I probably lean yes.