One of the reasons why it would be so hard is that Proof-of-Stake is not possible with a fixed limit for the amount of coins like the 21 million limit of BTC. A PoS coin would increase its supply infinitely. One can achieve some stability in coin supply by destroying transaction fees (like PPC) but a "hard limit" is not possible.
Of course it is. Just because PPC chose not to go that route doesn't make it impossible. It was a design CHOICE not a requirement.
The security model is based on coins (coin*days), it needs some coins amount to function properly. Non-deterministic supply is not a choice, it's a security requirement. Otherwise there will be no protection against massive coins destruction/lost wallets/whatever, i.e. no security in the long-term.
It isn't a requirement. How about coins have to be moved within so many years (say 10). Coins that aren't are deleted by the network and respawned as new miner rewards thus keeping the pool of coins available for stake relatively constant. That is just one idea. It isn't an absolute requirement. The creators even stated so. It is just one solution to the problem.