Except that agents with free will do not unanimously act alike. At least there's no guarantee of that and, with 100 billion free agents, to claim that they all happened to make the same choice as Adam is unlikely. Consider the angels. Many of them chose to fall, many did not. They do not act alike.
If all beings act alike, that's not freedom, it's caused by the nature of their design whose fault lies with the Creator.
Furthermore, if we all act alike, then you should pay for my sins as well. If I go commit a crime, you should be punished for it because, if we all act alike, you would have done the same thing.
By that same token, if we all act alike, God cannot differentiate between servants. He cannot praise one servant for a job well done while chastising another for disobedience or even mediocrity.
You've also get exegetical problems. Again, when Paul said that all sinned, there were plenty of fetuses in the wombs of his day. When did they sin? He is clear. They sinned in Adam.
If all men are born innocent, untainted by Adam, then Paul is wrong to suggest that they need a savior. All they need to do is walk faithfully.
Let's suppose we posit an age of accountability - let's suppose it's 5 years. If a child is still innocent at 5 years and then dies, didn't he make it to heaven by good works? Why the need for the cross, in his case?