If I understand your question correctly, that's not quite how it works.
Exersizing the option does not remove the fact that you have coughed up some extrinsic value (AKA time value) for it.
In fact, if you exercise an option where there is extrinsic value remaining, you immediately lose that extrinsic value. In all cases where there is extrinsic value remaining, (except where there is a financial benefit to exercise and capture a dividend) it would be better to trade out of the option to capture said value.
Even if for some reason you want the shares before expiry (and there is no divvie), and extrinsic value remains, it would still be better to sell the option and buy the stock in separate transactions... NOT exercise the option. Exercise only makes sense AT expiry, IF you want the shares ('cept for the divvie situation).