Did left-handedness keep Mark Grace out of the Hall of Fame?

Okay, completely out-there thought: Mark Grace appeared on the HoF ballot for the first time this year, and only garnered 4.1% of the vote, knocking himself off the ballot and guaranteeing that he'll never see the hall, unless the Veteran's Committee goes completely insane. His numbers don't really justify entry to the Hall of Fame...that is, at least considering that he was a first-baseman. However, Curt Schilling, in his blog, ran down the Hall of Fame ballot and said of Grace (in addition to him being the only teammate who talked more than Schilling), "Was literally a Gold Glove SS playing first base." Now, just because Curt Schilling referred to Mark Grace as a "Gold Glove SS" doesn't mean that he was one, but stay with me here for this thought experiment. Imagine a shortstop with a .303 average, .383 OBP, and a career 119 OPS+, with a peak OPS+ of 141. That's certainly not a lock for the Hall, but it's at least plausible. Suppose Grace really was athletic enough to play shortstop, but couldn't...because he's left-handed. Now, the easy rebuttal to this is that if he were that athletic, he should've played CF, which would give him extra positional value without requiring right-handedness. My rebuttal to that would be that probably the most important attribute for a centerfielder is speed, which Grace notably lacked, but shortstops can get away with less speed.

Admittedly, this ultimately comes down to a "If my aunt had balls, she'd be my uncle" argument, but it's something I've thought about a few times and found it interesting. Sometimes there's a lot of randomness involved in baseball.