Allen's offensive WAR per 100 games is just over 4. No other third baseman whose career started after 1900 achieved that. Schmidt is at 3.8 and Eddie Mathews at 3.9. Among other third basemen who were not very good defensively, Brett is at 3.1 and Molitor is at 2.8.
Want to consider Allen as a first baseman? His 4.0 WAR/game ranks second all time, to Lou Gehrig. He's ahead of Foxx and Greenberg, Among other first basemen who were defensive liabilities, Frank Thomas is at 3.5, Thome is at 3.1, Killebrew at 2.9, McCovey at 2.8, and Cepeda at 2.4.
The complete list of other with over 4 offensive WAR/game and 1500+ games played is Allen, Gehrig, Bonds, Ted Williams, Cobb, Mays, Speaker, Mantle, DiMaggio, Ruth, Aaron, and Musial. Trout will join them when he gets to 1500. Those guys are not run of the mill Hall of Famers; they are immortals.
I think Allen has three things going against him.
First, he was a bad defensive player. But there are plenty of bad defensive players in the Hall of Fame, and most of them were not as good as Allen offensively. His career WAR is dragged down by large negative defensive WAR, but in my opinion, dWAR is much less robust a stat than oWAR, and even more so for players who played many years ago.
Second, his career was relatively short, and that hurts his traditional counting stats. But he still put up more offensive WAR than most Hall of Famers, and more total WAR than probably 30%-40% of them, even being penalized by a bad defensive WAR total.
Third is his mixed reputation, some of it earned and some a product of having to deal with racist fans (and in some cases, teammates). On the other hand, we have Hall of Famers who are convicted criminals, racists, and PED users, most of whom were worse players than Allen.
I am not really objective when it comes to my first ever favorite ballplayer. But I think this information shows a very strong case for him to be in the Hall of Fame.