Why is that? The FED obviously has levers that it can push to lower inflation. Currently, the levers are kind in a tricky place. But if they let inflation run its course now, and then push the levers later, wouldn't it be effective?

> if they let inflation run its course

What other posters are telling you is that there's no such thing as letting inflation "run its course." What actually happens is that high inflation becomes baked into the normal operation of the economy, at which point it is extremely difficult to get rid of (i.e. not just raising interest rates above the inflation rate).

This isn't true at all. Look at french inflation figure during the post-war boom. We have lower inflation right now than back then.