What is the reason that the new coins should be given in proportion to existing coins, iff the holder also does some work?
If the work done is equivalent for 1 and 10,000 coin holder, should the reward not be also?
This is hard to arrange. A rich miner with 10,000 coins could split their holding into 10,000 wallets of 1 coin each, and present to the network as 10,000 poor miners, and there-by get 10,000 times the reward.
Are we rewarding from the work, or just instituting inflation? If latter, what was the point exactly..

PoS is no more inflationary than PoW. Go re-read the first post in this thread. The idea is that exactly the same number of coins gets created in each block, presumably with the same block-reward halving schedule.
We do need to reward the work, to keep miners mining, so that transactions keep getting validated and coins keep flowing. However, the deeper motivation for PoS or PoW is as a solution to the Byzantine Generals Problem. Basically, in a distributed system, conflicts are resolved by majority vote, and voting has to be made expensive to prevent stuffing the ballot-box. Proof-of-work is one way to make it expensive. Proof-of-stake is another.