Pure proof of stake is not secure, because somewhere in the workings of it there has to be some kind of random or pseudorandom number generator used to decide which staking client wins the/a stake on any particular block.

Someone with more computer power can explore multiple possible futures, generating billions trillions quadrilions etc such random or pseudorandom numbers, massively increasing their chance of having their stake, of whatever size, "get lucky".

This is pretty much a pure nature of the problem kind of problem, not only has it not been solved it probably is not solvable.

That is why proof of stake coins that make even a token, propaganda-style pretence of being in any way even slightly secure (such as ppcoin for example) have a proof of work element in them, they are not pure proof of stake and admit that it is because pure proof of stake cannot be secure that they are a hybrid, having proof of work as well as proof of stake.

Worrying about how to initially distribute coins you know a-priori are never going to be able to be secure is basically a waste of time, a mere thought-experiment about an inherently useless and pointless "product".

You might just as well work on how to distribute sewage to as many individuals as possible, or how to drop a brick on the head of as many people as possible etc.

-MarkM-