We baseball fans love us some stats. Sometimes they seem to be more important than the players themselves. We use them to measure the abilities of players against their contemporaries and, with adjustments, against players of other eras. We use them to decide who is worthy of election to the Hall of Fame. And they are a large part of the anger at those players who used PED's. By doing so they destroyed the meaning of their statistics when compared to other players. Barry Bonds hit 762 home runs? Hank Aaron might have hit a thousand if PED's had been available to him. Don't even think about including PED users in the Hall of Fame. Their stats should be buried in a deep, dark hole and never spoken of again.
You want an unfair advantage? How about playing in a league that obscenely excluded many of the best athletes available? How many home runs might Babe Ruth have hit against a talent pool that included black players? You can be sure that it would have been less than 714. The integration of major league baseball was not even done equally. In 1965 the National League had 15 black Hall of Fame players on the field. In 1965 the American League had 0 black Hall of Fame players on the field. This imbalance was slightly adjusted in 1966 when Frank Robinson was traded from Cincinnati to Baltimore, making the count 14-1. Robinson immediately won the Triple Crown. Keep this in mind when making your argument that Mantle was better than Mays.
So, the only 'pure' period of baseball would run from the mid to late 1960's until the early 1990's. Unless you want to consider that rampant amphetamine use might have sullied this era too. Go ahead, you might as well. If you only allowed players whose careers were confined to that range of years you're going to have a very small, very lonely Hall of Fame. Of course you wouldn't need to allow much time for touring the building.
Here's the thing. Forget about who hit the most home runs or who had the highest batting average or who had the lowest earned run average. Those numbers have no meaning across eras. I hate it, but what are you going to do? Forget that the Babe played against a severely diminished talent pool? Forget that Hammerin' Hank played against a somewhat less diminished talent pool? (Admittedly, since Aaron played in the National League, his stats may be as good as you're going to get as far as a level playing field.) Every major league player in the Hall of Fame had stats that were tainted in one way or another.
Consider each player within his time. Remember that attempts at performance enhancing likely go back to the 1800's, whether or not they had any effect. Forget about PED use as a disqualification. Let those players go into the Hall of Fame without asterisks. If you're really so gung ho to use those little stars put them next to the players who played in a segregated era. They may have thought that there was nothing they could do about the situation but they certainly reaped the benefits.
Check out Baseball Integration, 1947-1986, an article written by Mark Armour for the Society for American Baseball Research in 2007. I stumbled across it some time back. It doesn't just concern itself with the number of black players but also with the quality of those players.