I guess it depends on what you mean by public circulation. QE was certainly effective in raising the amount of reserves, since that is what it is by definition.

I guess it depends on what you mean by public circulation. QE was certainly effective in raising the amount of reserves, since that is what it is by definition. But reserves are only ever held by banks. The amount of money held by the non-bank public has not been changed significantly by QE. As for targeting the money supply, you're right, they could do that, and in fact they did try it a few decades ago. The problem that was observed is that it created extreme volatility in the interest rate. The lesson learned from the experiment is that either the interest rate or the money supply has to be volatile, and there's general consensus that a volatile interest rate hurts the economy, whereas a volatile money supply has marginal effects at best.