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Without the separate ground on the mast ALL of the current it may collect in a nearby strike WILL go into the coax.
A separate more direct and larger ground wire from the mast to the ground rod will divert more of this current and help keep it outside your house.
Remember only the outer braided part of coax is grounded, the center copper wire is not. It will carry some current too, you want to divert as much as you can to something else.
As rabbit stated, no grounding system is 100% effective and a strike close enough or direct will not be stopped. You'd have to make your house a giant 10 million volt capable Faraday cage to stop a direct strike.
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