Who defines what qualifies as good/poor character - the press, social media, the voters? Likely all three - this means that "good" character 20 years ago might be considered "poor" today and "good" today might be "poor" 20 years from now - or even next year.
Unfortunately, in a society that has taken to destroying a person's life when possible for "poor" decisions, it seems character is an important factor when a group decides to raise a person up as a "hero" or as "one of the greatest." I'm sure the HOF wants to avoid negative press and backlash.