Keep in mind that large miners need to recoup large costs. As they sell newly minted coins, that increases distribution.
...but this doesn't make the distribution more flat which could be considered fair. What would be the purpose of just putting more coins out there. If there would be no new coins newcomers would just buy them from old stakeholders.
Money will never be "fair" in ways that makes everyone happy. If your argument for using PoS coins that it is a more fair way of distributing wealth, I guarantee you that you will be sadly disappointed if PoS ever goes "mainstream"