Not only this, but also ICBMs

Here's an article saying that ballistic missiles can be shot down by "howitzers".

Sure, why couldn't they?  All you need is where to intercept, and by golly, you can do it.  Today's computers can calculate the trajectory and launch an intercept that will knock down a shell.

So, why can't they do this as a terminal defense for an incoming ICBM?

There's no reason they couldn't.  Most people don't get this because they don't know how nuclear bombs work.  You won't make it explode if you destroy the warhead.  Nope, you KEEP it from exploding.  It gets its power by being confined in a small area.  If you "blow it up", you prevent it from becoming as dangerous.

I'm convinced the idea could work and make ICBMs obsolete.

Powerful lasers may be even better.  The incoming warheads are at their most vulnerable as they approach their final target.  Melt the warhead and it breaks apart.  A ground based laser can be fired at the warhead and kept on it until it begins to break up.  When it is time to explode, it becomes a dud.

The Hunter Gas Gun can definitely hit it with an awful amount of force that cannot be defended against.

It is taken for granted that an ICBM attack cannot be defended against.  But that's wrong.