The Bretton woods change was to allow stimulation of the economy - because things at home were losing momentum (relatively speaking) as other countries manufacturing bases and economies recovered from the damage from WW2. It was a way of keeping the US a few steps ahead.
Printing gold backed dollars quickly doesn’t work very well when you can’t increase the rate of mining gold quickly. Non gold backed dollars are a lot easier.
As long as goods and services can be made cheaper every year, it works well since inflation isn’t felt badly - there aren’t any supply restrictions where something is going to get noticeably too expensive.
All the things I talked about though all have that issue - they can’t be made cheaper somewhere else. someone can only build so many houses in LA before there is literally no more room, and someone building a house in Shanghai doesn’t help anyone in SF live closer to work. Building a new college/university in Vietnam isn’t going to help a kid in Oregon get their degree.
We’ve been exporting inflation because it’s worked. But when other countries stop being so much cheaper, or costs of critical things for the population finally exceed affordability, it doesn’t.
Yellen, Powell, and others are just following the rules and mandate they are given.