I really didn't want to get into the details of inflation even I had in mind what you suggested. The post would be extremely long. I agree. I merely wanted to make a point that not much would change if everyone was given one million dollars aka "if everyone was ending up being a millionaire".
When it comes to the zero sum fallacy because forget the gap of wealth. Sure everyone is getting wealthier but what matters is the difference between the peers — and as we all know millionaires and billionaires are increasing while the poor and middle class are merging together.