[qalmakka]

This, exactly. The Greek alphabet is much older than Koine Greek, of almost 500 years. While spoken language tends to change fast, written language tends to stick and doesn't easily change, for obvious reasons (just look at English or Tibetan). People won't change how they write some word just because they pronounce it differently from the past, because that would make the text much harder to read.

Also, /b/, /β/ and /v/ have the tendency to get swap with each other in lots of languages, and most people fail to distinguish them apart unless their language imposes a clear distinction among them. See for instance how Italian or English distinguish /b/ from /v/, while /b/, /β/ and /v/ are all basically the same thing for a Spanish speaker.