Someday a player is going to get in who has been uncaught, even unsuspected, but was secretly a user. It may well have happened already, and if it hasn't, it will soon. (I have no specific person in mind, but I have doubt that it will happen, whoever it may be.) Because of that, I am sympathetic to the idea of an amnesty for all pre-2005 steroid-era players. There will never be any way to separate the guilty from the innocent.
A-Rod, though, is not merely a known PED user from the pre-2005 era of an unenforced no-teeth rule; he is the leader of a ring of PED users who brazenly defied a clear and enforced post-2005 rule and then lied about it repeatedly. The character clause of the Hall has been pretty much a dead letter (except for Shoeless Joe Jackson prior to the 1991 rule formally excluding banned players), but if it applies to anyone, it should apply to Rodriguez.