The same applies to Eth2's PoS network, as block proposers are randomly selected with on-chain randomness. Block rewards are also not a major source of income for a staker on Eth2 — the majority of income (>90%) comes from simply attesting the chain correctly. This attesting occurs once an epoch for every validator, or every 32 blocks.
>Proof if stake is either really proof of work that is less secure and obscured, or more often dimply giving the creators of the coin the power and your trust....
PoS vs. PoW is really only a matter of how you ensure your chain can't be attacked. For PoW it's equipment cost, burnt electricity, and opportunity cost for losing rewards due to attacking the chain. For PoS, the security is ensured through a high-enough buy-in cost (32 Eth), and penalizing attackers harshly through slashing.
You can imagine how expensive it would be to accumulate enough Ether to attack the current PoS chain. There is 3.3 million Ether staked across over 100,000 validators, and one would need more than half of that total stake to have a chance at attacking the network, a failed attack resulting in massive slashings. This is made even harder as the attesting validators are shuffled continuously.
I personally loathe the energy consumption of PoW, and believe PoS to be the future. The fact that hundreds of validators can be run on just 5 watts of power should say enough.
If all validators on the current Eth2 PoS chain were run on individual machines, the energy consumption would be ≈4.4 GWh yearly vs. the current PoW chain's ≈25 TWh — a 5000-fold decrease. This is decrease is in reality probably even larger since pools, decentralized and centralized, will be running multiple validators on a single machine which affects resource usage very minimally.