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.
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.