control theory niggas i need some help...

so if i'm given any transfer function can't i always put it into controllable canonical form? what transfer function can't i put into any of the canonical forms? i can always do it. so then,
>This state-space realization is called controllable canonical form because the resulting model is guaranteed to be controllable
So all transfer functions are controllable... ? So what's the point in testing controllability of a system if literally all systems are controllable? I'm lost bros