One of the workhorses of international macroeconomic theory, the Mundell-Fleming model, dealt with precisely this issue some 40 years ago. And you are familiar with the result that, as long as you operate a flexible exchange rate, monetary policy becomes the more effective the higher the degree of capital mobility is.
The exchange rate channel then more than compensates for the decline in the ability to influence long-term rates. Second, one might debate whether influence over long-term rates is the most important way in which central banks achieve their goals.