If I literally stole 1 trillion dollars from the richest Americans and gave it to the poorest 20 million Americans, I'd have substantial impact on the standard of living (both for them, and for the country on average).
Ignoring the fact that there isn't just $1 trillion cash sitting in a vault somewhere, after your 20 million American's burned through their $50k, they'd be back to square one.
Think this through; is Somalia poor because their government doesn't give poor people enough money to consume?
No. Somalia is poor because they produce very little right now (for a variety of reasons). If you look at countries that have recently increased their standard of living on a massive scale, such as China, they have done so not because they consumed their way there. A huge amount of investment into productivity was undertaken.
> Ignoring the fact that there isn't just $1 trillion cash sitting in a vault somewhere,
When my team of 100 crack assassins/financial shenanigan wizards target the richest 100 Americans individually in their own homes, I don't think this will matter too much. We'll get the money.
>after your 20 million American's burned through their $50k, they'd be back to square one.
Sure, but their standard of living would meanwhile have increased.
Obviously, it's a reductio ad absurdum, but I'm using it to prove a point.
Your use of Somalia merely proves that a certain level of productivity (shall we call it GDP?) is required for this thought experiment to even make sense. Yes, a certain level of society-wide wealth is necessary for redistribution to even be possible. And indeed, one could try to improve productivity instead of or in addition to redistribution.
But none of that means that in a society with as much productivity (a high GDP, if you like) as the USA, redistribution could not also be used to increase the standard of living.