It happens all the time when you're working with substrings. Under your encoding, "é" would be a substring of "ჩ":

           10000011 11101001 U+E9 "é"
  10000001 10000011 11101001 U+10E9 "ჩ"

This would make it incompatible with many existing processes that already handle text, which was one of the goals of UTF-8.