Fred McGriff had maybe my favorite nickname among players in my lifetime, The Crime Dog. I like it because it has semi-random roots, stemming from McGriff sounding a lot like McGruff, the name of a cartoon dog that was supposed to keep kids safe by informing them about crime... or something. That's what the backstory to a nickname ought to be, not "We took his first initial and connected it to the first syllable of his last name." Additionally though, if you're unfamiliar with the 1980 creation of the Saatchi & Saatchi ad firm, the name still just sounds cool. Alas, an awesome nickname probably isn't enough to build a Hall of Fame case on, so I'd better dig a little deeper...
The case for McGriff as a Hall of Famer
McGriff hit 493 career home runs. The only players who've been on a Hall of Fame ballot before who hit more than that and aren't in the Hall of Fame are Barry Bonds, Sammy Sosa, Mark McGwire, and Rafael Palmeiro, all of whom have pretty strong evidence tying them to performance-enhancing drugs. Offense reached an historic high in 1994 (then kept going up for a while), but McGriff had already put in his best seasons by then.
He hit 30+ home runs in seven consecutive seasons (1988-1994), easily leading all of MLB with 242 of them during those years, far more than Barry Bonds' runner up total of 218. McGriff is also among the top four in RBI, extra-base hits, total bases, and walks during those years. He's 9th in OBP (.390), 4th in SLG (.545), 3rd in OPS (.935) and wRC+ (153).
Only Bonds, Thomas, and Rickey Henderson were better offensive players during that time, and those are three of the greatest offensive players in baseball history.
As his rate stats for those years show, he wasn't just a home run hitter, he also smacked a lot of doubles (441 for his career) and drew a lot of walks (1,305).
McGriff's career OPS+ of 134 is very impressive for a player with 10,174 plate appearances, because the longer you play, the more your rate stats tend to drop. Among HOF eligible players with even 9,000 PA, the only ones with an OPS+ as good as McGriff's not in Cooperstown are Bonds and Jeff Bagwell, both of whom would likely be in if not for PED connections (be they real or imagined).
The case against McGriff as a Hall of Famer
Those seven years look awfully good, but if you expand to a wider timespan, McGriff's standing drops. He had only two additional seasons with an OPS+ better than 125, and while figures in the 115-120 range are good, they're not great.
The bigger problem for McGriff's case is that while he had a great career at the plate, he didn't really provide any other value. He never stole more than 8 bases in a season, his career SB success rate was a weak 65%, and advanced metrics have him as below average on the bases for most years of his career, and also have him as a below average (or bad) defender at first base, a below average defensive position.
His career WAR total (52.4 at Baseball-Reference or 57.1 at FanGraphs) is better than that of some first basemen in Cooperstown, but pretty well below the average.
My two cents
I think McGriff's quality as a hitter is generally overlooked these days, due to bad timing on his part. He put up really good numbers for a fairly long stretch, but he did it just before changes in the game made those numbers look somewhat pedestrian. I think he's one of the 60-70 best hitters ever, and that should get someone awfully close to the Hall of Fame all on its own. McGriff just doesn't have enough else to go with that great hitting though. For me, he's Hall of Very Good, but not quite Cooperstown.