I don't disagree. Effects and implications for the fx are very important. This was the problem with operation twist. No one wanted to buy short bonds, since longs werte equally liquid, and had a higher return. If the Fed would fix the short rate and also shape the bond yield curve, then I suspect the fx rate might slip completely out of control.
Long rates go up when funds leave the bond market.
A good portion usually goes abroad, I would say, depressing the fx rate on their way out.