What is the basis of the change in Rashi's letters from the standard Hebrew ones?
And if it was something that was dependent on a specific factor then, why weren't they changed back?
Who says that it's a change? If you consult Ada Yardeni's The Book of Hebrew Script (The British Library, 2002), you'll see that the shape of Hebrew letters has been evolving over the millennia. According to The Hebrew Book: An Historical Survey (ed. R. Posner and I. Ta-Shema; Jerusalem: Keter, 1975), Hebrew printing only began in Italy in 1475. The first book ever printed, around that time, in Reggio di Calabria used a semi-cursive font that was popular in that region, and which only came to be known as "Rashi script" because the text in which it appeared was Rashi's commentary on the Pentateuch. The first Hebrew book to be printed with square script was printed 26 years later, in 1501!
In time, the custom of utilising "Rashi script" as a commentary was maintained purely in order to differentiate the commentary from the actual text itself, but asking why it didn't get changed "back" would be like asking why the square script didn't get changed back into one of the dozen or so different scripts that preceded it.