1) a pure PoS system starts with the creators holding all supply and can keep an arbitrary portion for themselves while selling the rest as they please
2) the truth in PoS is subjective (nodes need to rely on other nodes to determine what is the current state of the system).
A) in PoW you
A1) either put all your resources (hash power) behind one chain, and get the block, thus the mining reward, with probability equal to your proportion of the total hash power (as before) assuming that chain ends up the longest chain (so you have a strong incentive to pick the "correct" one), or
A2) distribute your hash power between the two competing chains, but then each of them only gets half the hash power, and you reduce your probability of getting the mining reward to half, thus halving your expected reward.
At any rate, as soon as one of the chains is ahead, there is a very strong incentive to fall in line with the LCR (longest chain rule) and place all your bets on the putative winner, rather than diluting your expensive hash power.
B) In PoS, you can just continue staking on both competing chains, and whichever wins, you got get your mining reward (as usual, with probability equal to your proportion of the total stake). No incentive to settle on a winner early ("nothing at stake"), so just keep your options open by supporting both chains, and thus no incentive to congeal on a winner quickly.
As for layer 2's this could partly be the solution to some high costs. But risks sacrificing decentralization.