Low barrier to entry - Allows anyone with coins and running a fullnode to participate
Pooled mining not possible without custodial risk?
More decentralised because it incentivises currency hodlers to run a full node for mining rewards
Cons:
Insecure - All solutions thus far require some form of centralisation (authority/checkpoints) or trust, something which is unacceptable for Bitcoin.
Nothing at stake problem allows large stakeholder miners to mine all possible forks, eventually find a fork where they come out on top, allowing them to rewrite history at point in future.
Not suitable for coin distribution as the first recipient of coins can always rewrite the entire history at any point in the future due to the fact that he owned 100% stake at one point of time.
Unlike POW, cannot objectively determine best/longest chain as there is no real cost to produce a larger chain(Nothing at stake). Resulting in checkpointing by trusted parties
Your economic assumptions regarding POS are incorrect: