In the case of George Burns, I am not so sure he'd be as interested in playing the game as he would be in telling funny stories, and that's not what HS is about. Also, I think Burns would be out of place as a panelist, because Burns is a straightman. He'd be unaccustomed to cracking jokes. George didn't do many game show apperances. He appeared once on the 1972 version of IGAS, and his secret was that he tells lies. Unfortunately, George was really just doing his schtick and not playing along with the secret, which noticeably annoyed Steve Allen.
Jack Benny also did few game show appearances. He definitely would've been a good celeb if they wrote questions in tune to his stingy character.
I think it's interesting that Milton Berle appeared on game shows at all. Peter Marshall said in his book that Milton thought game shows were "above him", but at the same time, Milton's popularity on TV pretty much declined once his show went off the air.