In PoW, the coins are minted steadily by miners from all around the world. The minted coins are initially distributed to the miners, and then spread to more people in circulation. In PoS, because the block mining is associated with existing stakes (coins), there must be a process of issuing seed stakes. In the early stage, the issued stakes might bear high capacity of generating new coins. The stakeholders are likely to be reluctant to sell stakes at hand. Therefore, issuing all seed stakes at once in the beginning may result in an inert market environment, jeopardizing the further distribution of the stakes.
I think a more reasonable mechanism is to issue the seed stakes regularly (e.g. quarterly) in the first several years. Each time, a certain percentage of seed stakes will be issued, including all their mining awards so far. These regular stake supplies will open windows for new participants. The percentage may gradually decrease (like Bitcoin's supply control). When the seed stake supplies run out, most of the coins should have already been minted. At that time, the earnings from coin minting will be a minor factor compared to the market price variation, and thus the stakeholders will no longer be reluctant to trade their stakes. After the seed stake issue has finished, the running of the transaction system will be fully decided by the PoS protocol and free market.
What do you think is the proper way to distribute a PoS coin?