Why is "trimming" a carbon compositon resistor not possible?
You can. In fact, long ago, when resistors were not nearly as readily available as they are today, it was not an uncommon technique.

Filing a notch into a composition resistor will increase its value, but it will also have detrimental effects on its mechanical strength and long-term reliability. Seal the cut with lacquer and mount the resistor such that there is no stress on its leads.

Of course, today we have access to precision resistors at very low prices, so there's no longer any reason to do this.

(I'm not sure why the other answers and comments are talking about film resistors, since you asked specifically about composition resistors, which are constructed differently.)