They are correct that proof-of-stake doesn't solve the initial wealth distribution problem. ADA and XTZ solve it by pre-mining the coins.

Ethereum is instead solving it by having an initial proof-of-work period and then moving to proof-of-stake after some amount of mining and wealth distribution has already happened.

That's not what they said. They said POS can't distribute coins, which is not accurate.

ADA and XTZ did pre-mine their initial distribution, and now they distribute coins through stake rewards.

That's not distribution. That's just letting every owner maintain their share of the pie by staking.

You can argue whatever you want, it's distributing coins to the people who secure the network.

So, PoW then.

They secure the network by showing up and participating with minimal calculation. I don't think that falls under proof of work. Even if it does, it's not the terminology that matters. What matters is that there is no reward for burning cycles.

It’s not POW. No need for massive amounts of processing power. Read IOHK’s Ouroboros paper or Breitman’s Tezos paper.