Natural reproduction is never about creating perfect copies. Far from it, evolution gives rise to genetic drift, a process through which the genetic pool in small populations varies due to a random selection of genes. The more organisms reproduce, the higher the chance of variation, in both small and large populations.
Script shifts, too, but only when it is subject to similar laws, which really affect only handwriting. Today we use handwriting for strictly private purposes, while sharing it less and less with others. We write brief notes on a piece of paper to give to family, friends and colleagues, but the days of writing long letters in controlled script, going for several pages, are long gone. Making one’s handwriting public is an extraordinary thing and is usually restricted to exhibitions and art galleries.
A manuscript-dominated culture of literacy means that most if not all writing is handwriting. Script is generated through direct human input and depends on cultural reproduction – rather than mechanical replication – to survive from one generation to another. Handwriting is organic and shifting all the time. While print hasn’t shifted too much from the 16th century to our own day (proof being that anyone who can read this blog can read the letters of an Italian printed book from the 1480s), handwriting had drifted and changed considerably during the period before. If you manage to read 14th-century Gothic script, that is no guarantee you can decipher the letters of 8th-century Beneventan script or, worse, Roman cursive of the 1st century AD.
During the long manuscript age of Western Europe, writing was in a constant state of flux. The more Europe wrote, the more script shifted. The evolution of script is still a hot topic to historians and palaeographers, who are constantly discovering ever smaller shifts in local scripts affecting the general evolution of writing.
The Latin proverb Verba volant, scripta manent is right. Spoken words fly away, but written words remain. However, the script of those very written words often flies away, too. Nothing is ever really set in stone.