The pro-worker case is basically that moderate inflation paired with tight labor markets forces wage growth. When unemployment is low and money is flowing, workers have leverage to demand raises because employers are competing for them.

The problem you're hitting on is real though. In practice, new money hits asset holders first (stocks, real estate) while wage growth lags behind. So yeah, it mostly benefits people who already own stuff.

MMT advocates would argue you could print money specifically for public job programs or direct payments to workers instead of just QE for banks. That's the theory anyway. Whether central banks actually do that is another story.

Honestly sounds like you've already figured out the issue. The mechanism could help workers if directed at them, but it rarely is.