Seems to ignore the fact that picking up and putting down the writing point is actually harder for small children than just sliding the writing implement along the paper. Also consider the popularity of "Swype"-style keyboards, since continuous sliding a finger across a surface is, for many, easier than discrete screen presses.
Sources: personal experience and anecdotes from teachers of 4-6 yr olds (an age range not given the most, if any, time in the article).