It is harder all right, as you can see if you watch the various attitudes that left-handed people adopt when writing, especially when writing in liquid ink, that easily blots or smears if you touch it before it gets dry. We see less of that nowadays because of the nearly universal use of volatile inks, such as in felt tip pens, and inks that soak in almost immediately, such as ballpoint inks. Right-handed writers have their hand clear of the paper where the writing is to happen, but a left-hander's hand passes over the surface where he has just written.
It also is easier for right-handers because they can see not only what is happening under the pen tip, but the last few letters of what they have written, which are hidden by the hand of a left-handed writer.
Apart from writing from left to right or right to left or, for that matter boustrophedon, in which one alternates (an attractive idea, I always thought!) at least some common scripts go from top to bottom; I do not know how many other variations one gets. I have a few ideas for better schemes, but I am sure that everyone has far too much seems even to consider them, given the preponderance of right-handers and the dominance of tradition and custom. There is a huge number of possible variations, including spirals and helices, not to mention the scytale and similar transposition encryptions! :-)
My personal impression is that each of these conventions originated, incompletely considered, with the whims and preferences of the first calligraphers in each script. They, after all, had no hindsight to warn them of the unfortunate consequences for ease of reading and writing, much less what a huge volume of reading and writing would follow according to the customs that they were instituting.