What would happen? Some will instantly sell, while others will buy, some will hold, some will spend, and some will lose them.
So within months, there again is an uneven distribution. Which then in time will be considered 'unfair', because some would argue they needed the fiat, did not fully understand Bitcoin, got robbed, etc etc.
What you are suggesting would be "fair" is similar to socialism (everyone getting the same number of bitcoin).
To see how this would not work see The tragedy of the commons (this is not a play)
http://en.wikipedia.org/wiki/Tragedy_of_the_commons
EDIT: nor is it shakespeare
And for a practical example, playing out in the world theater as we speak, for everyone who wants to see, look at Venezuela.
Look at the United States. Look at how many people have enrolled in so many social programs since Obama took office.