Not the rate of interest, but the cost of finance. Not inflation, but the decline of growth.

It is surely true that the price level cannot rise without a corresponding increase in the quantity of money or velocity or use of credit. But to deny that real costs matter (as many people do) is a problem, for rising cost hinders growth.

In a simple example where finance is non-productive and adds nothing to the economy but cost, growth of the financial sector is inflationary. But even if finance is only in part non-productive, the growth of finance is still in part inflationary. And either way, the inflation is cost-push. 

Unlike demand-pull inflation, cost-push shifts the aggregate supply curve to the left, reducing output. If the Fed fights this inflation by raising rates and slowing the economy, output is further reduced.

Furthermore, in a society with an expanding financial sector, the growth of finance is a "sustained" event, not "temporary" like an oil shock. Thus the resulting cost pressure is sustained, the cost-push inflation is sustained, and the decline of economic growth is sustained.

In such an economy, the best you can hope to achieve is sustained low-level inflation along with long-term slowing of economic growth. 

It is slow growth that kills civilization. Inflation is just evidence of the problem.

If the growth of finance is the problematic cost, then suppressing demand will not solve the problem. Only reducing the incentives that drive the growth of finance will reduce the cost pressure, solve the inflation problem, and restore the forces of economic growth.