The thing with non-Roman alphabets (excluding written languages from other areas like say the Chinese-derived symbol scripts) is that they were created with specific needs of a spoken language in mind. For example, Cyrillic has specific letters for certain sounds that exist in Eastern Slavic languages such as Russian. The sounds "tz" and "ch" have a single letter to represent the sound, for example. Scandinavian alphabets use certain symbols that "modify" a Roman-derived letter to represent a certain pronunciation of that sound.
In medieval English, there were a few letters that were used to represent certain sounds, such as a runic character that looked like an uppercase D that represented "th". As late as the 19th century, there was a "long S" letter that was used to represent the "ss" sound. This letter can be found in USA's founding documents-in the early days of the internet people would scan cheap copies of the Declaration of Independence and the Constitution directly into computers, and the early programs couldn't handle the lowercase version of the "long S", which tended to come out as a lowercase "f". Standard German still has a separate letter for the "long S", that looks like an uppercase B.
What would be interesting to see is an adaptation of, say, Cyrillic to English, in fact when part of Romania wound up inside the USSR after WW2 the Russians adapted Cyrillic to the Romanian language. And then there's the Deseret Alphabet, created in the 1850s by the Mormon Church as a way of isolating the faithful by making them unable to read Roman characters. Now that I think about it, what would be REALLY awesome would be to adapt the cuneiform-based alphabets of Armenia and Georgia (the country) to English.
