Because you need to purchase the out of the money side before you can exercise the in the money side, otherwise you lose the optionality. That is the entire point of the early exercise formula. It is to determine cost of carry of current position vs. theta of transferring that optionality to the out of the money. Think about a high dividend issue with several weeks to expry. Then think about exercising early, not picking up the otm option, and watching the market crap. OR maybe easier to perceive. Think of those deep calls being against short puts a strike away, exercise those calls and then run a downside risk scenario and you will see why you needed to buy those puts.
The trade-off for early exercise must ALWAYS be analyzed with buying back the OTM.