Shooting down supersonic, hypersonic, and stealth missiles is hard. You may need to fire multiple anti-air missile just to hit one attacking anti-ship missile. But doing so depletes your magazine faster and it can just come down to who has more ammo.
If you’re able to fire a couple anti-air missiles, and then recover the ones that miss, or have them loiter and acquire a new target, I could see that as being an advantage.