This is the sort of missile a fighter pilot is up against, 20 years ago. Look at what the sidewinder does at about 1:05. Good luck shooting that down.
Impact energy grows with the square of the velocity. If the velocity doubles, that is like quadrupling the mass of the bullet, which is like turning 20mm ammo into 32.75mm ammo.
It's not like a small flightless ant on radar, and anyway a Mach 4 object will be hot from compression heating. Mach 4 is just below what it takes to rip air molecules apart. That's damn hot. IR tracking would be trivial.
There is no limit that says "one bullet only". Typically the Phalanx CIWS fires about 100 shells, and those aren't even equipped with seekers. It's just dumb 20mm shells, about the same as carried by the typical fighter plane, costing about $30 each. We use the Phalanx CIWS against incoming missiles. It works great.
BTW, that was an unimpressive video with no clear point. Yes, missiles can fly and go after targets. We all know this. It works especially well in the missile vendor's promotional video.
I think you're forgetting that a lot of anti nuclear defense systems use nuclear weapons themselves. When you only need to be within a few hundred meters of a target accuracy suddenly doesn't matter at all, especially when you have several hours to predict the flight trajectory of the enemy missile.
If laser based CIWS turns out to be viable on aircraft then we would see a focus on bigger aircraft that can defend themselves against missiles but even then they would not directly fly into a missile if they can avoid it.
The systems to use nuclear warheads against incoming nuclear warheads were decommissioned half a century ago. I don't think that was ever in use against satellites.
Lasers are nice, but definitely not needed. Phalanx CIWS uses about 100 unguided bullets to destroy an incoming missile. Modern US fighter aircraft carry the same diameter ammunition. The plane is like a flying CIWS, minus the software.
Eh, maybe minus the software. If the software existed, it might not be public. Maybe the F-22 or F-35 already have the capability, limited mainly by pilot G-force survival.
You said the missile had some amazing ability to turn, and now you're saying it has no fuel. You can't have it both ways. There is fuel, or there is no energy to spare. Being "cold" isn't generally possible; nothing cools instantly. Modern IR sensors do not rely on engine heat. Supersonic flight generates plenty of heat on the nose.
That last bit deserves more emphasis. Heat was a serious problem for the Concorde and SR-71, despite operating at much slower speeds. The missile is hypersonic. That is the speed at which air molecules come apart from the heat. IR detection will be trivial.
There is a circular circuit board that is very much needed for the proximity fuse. That is full width.
The speed of the missile contributes to its own destruction. Bullet impact will be devastating. The missile can not endure supersonic flight with a lopsided hole and a bunch of cracks, and it wouldn't fly straight even if it could. Tumbling means instant destruction, like Space Shuttle Columbia.
Shooting back is the action to maximize chance of survival. It takes priority; all other options are obsolete.
It becomes slightly more reasonable if you turret the gun, until you factor in the weight of the necessary ammunition to neutralize multiple threats, the turret itself, and the independent radar used for target acquisition and tracking. A B-52 could pull it off, a fighter couldn’t yet. Not without massively compromising their payload and aerodynamics.
Chaff, flares, stealth and jamming are used because they actually work in practice. Jamming is a big one that people don’t hear about much. Wonder how the B-52 is still in service? Jamming. Wonder how wild weasels do their job? Jamming.
When you see a turret like that on a bomber then you can get excited for self-guided bullets shooting down dozens of multiple incoming missiles. But tbh at the rate we’re going it’ll just be a laser instead.
Don’t modern missiles use optical target acquisition in the first place?
BTW, tanks have active automatic ballistic defense systems for a while now.
It is more common to have active electronic systems. For example, one such system fires grenade-like projectiles upward that then explode in a downward direction. The timing is accurate enough that the incoming attack is hit by the shrapnel. Another system is more like a shotgun.
The more reasonable comparison is ship-based defense systems. The USA uses the Phalanx CIWS, which fires simple dumb projectiles of the same diameter as those of a typical fighter plane gun. About 100 are fired to destroy an incoming missile.
Adding an AI to a modern fighter makes it an awful lot like a flying Phalanx CIWS. You have a nearly identical gun with a nearly identical radar.
That helps the defender. The faster the missile goes, the harder it gets hit by defensive shrapnel.
In case I'm not being trolled: the way to defeat a radar-guided missile is to beam (fly perpendicular to) the radar source. For an missile with active or semi-active radar guidance, this means you need to fly perpendicular to it. And, preferably, fire lots of chaff.
This is fundamentally incompatible with the idea of flying straight at the missile trying to shoot it with guns. Head-on, a missile will close the last mile in under one second. During this second, you need to accurately track, predict the flight path of, and reliably put guns onto a target that's cold (all the fuel has been burnt) and has (in the case of an AMRAAM) a 7 inch diameter. And that very well may not even care about being shot up with bullets; at best, I think you'd kill the seeker, but within the last mile it's not changing course much to have to come close enough to kill you by the proximity fuze (of which I believe there are two, one in the nose and one in the tail). By the time the first of your slow-moving bullets has any shot of reaching it, it will easily be within a quarter of a mile.
This is not even a remotely plausible way to defeat an oncoming missile. It runs directly counter to the actions you already be taking to maximize your chance of survival. And on top of that, bullets are only going to damage the leading-edge parts of the missile which aren't particularly critical to its ability to kill you, at least not within the distance it will be by the time your hail-mary bullet salvo hits it.