I would never see the shares as income, because you can "donate in-kind" by transferring ownership of the shares to the charity directly. The charity then inherits the cost basis and pays the capital gains when they sell.
It's important to note that I hold stock as an 83(b) election, not a stock option. Options can also be donated in-kind but that is even more complicated.
That said, it seems it wouldn't zero out my taxes. If donated to a public charity it has the potential to reduce taxable income by 50% for up to five years. That's still significant though.