Four letters of this alphabet write nothing Slavonic requires: ksi, psi, fita and izhitsa. Omega belongs with them in function though not in sound, since it duplicates a letter Slavonic already had. Together they form a distinct class, and recognising it explains a good deal about how the alphabet was used and why it was eventually cut down.
They exist for two reasons. The first is transliteration. The church books are full of Greek names and Greek terms, and spelling them with the Greek letters preserves the identity of the word, so that a reader who knows both languages can see through the Slavonic spelling to the original. That mattered for names above all, where a variant spelling can look like a different person.
The second is arithmetic. The Greek numeral series needs twenty seven signs, and these letters carry 60, 700, 9 and 400. Removing any of them breaks the number system, and for as long as the numbers were in use the letters were not removable at any price.
Both reasons weakened together. When secular printing adopted Arabic numerals the arithmetic argument collapsed, and when secular writing stopped being dominated by translated Greek the transliteration argument weakened with it. The letters went out of the civil alphabet within a generation of the numerals going, and stayed in the church books, where both reasons still hold and where all four are still set and still read.