Current is not quantiziced. Charge is because quarks has charges 1/3, 2/3 etc)I think unternensche got something right.
From QM energy transfer is quantized. It is said that as the number of aggregate particles of an object increases from the particle scale to our macro Newtonian scale the density of states is so high that things appear continuous.
The motion of a planet to us appears continuous, we quantify a planet's motion as a real number infinitely divisible as a practical matter.
IAW QM a planet can only change velocity in discrete steps. It takes energy to change velocity and energy is quantized.
We do the same with electric current. Current is Coulombs/second. Current is quantized, but in most cases we treat it as a continuous variable with real numbers infinitely divisible knowing it is not. The quantization effects are normally far below instrument's detection ability
Natter is quantized. If matter was continuous where would you cut it?
What he gets wrong is that quantum reality does not preclude an infinite number of objects or an finite unbounded universe.
Matter isnt quaticized but discrete.