When goods are short, we might expect profit margins to rise as the market rewards people who supply goods. If they aren't making extra profit, then there is no incentive to produce more goods.

A fairer interpretation of the situation is there is a lot of money chasing less goods. That results in, simultaneously, high inflation and reduced living standards. High profit margins aren't causing inflation - there have to be people able to pay the prices for raising them it to make sense.

Plus, the writer of the piece appears to work in wealth management. He's going to lose a lot of money if the fed doesn't drop rates back to 0. The author has a very strong incentive to argue as he does.