True, yet the existence of the Planck time constant does not really let us claim that time is necessarily quantized (here is a nice argument on this).

On the other hand, this does not mean it is impossible that the universe is a big computer with a discrete timestep either. Unfortunately, though, such a hypothesis is most probably unfalsifiable and hence outside the reach of scientific method.

From a practical perspective it makes most sense to consider time continuous simply because that's how it is postulated in most (probably all) physical theories today and these theories works totally fine.

Yet it is this continuous time assumption where the arrow paradox looks most paradoxical.