Y and B in Cyrillic

I've been toying with a crazy theory. Since the Cyrillic alphabet was based on Greek, the pronunciation of Cyrillic Y as oo may have been inspired by the Classical Greek pronunciation, which scholars believe to have been like French u or German ü. This sound is somewhat between ee and oo, with speakers of languages devoid of it sometimes hearing ee, sometimes hearing oo, and that's how it got into Cyrillic and the Slavic languages that use it, which have no need for the ü sound. Then the Y was lower-cased to y. A similar phenomenon may have affected Greek B, which was purportedly pronounced b in the classical period, but has evolved into a v sound in Modern Greek. Cyrillic B is pronounced v, which possibly suggests that betacism was already under way when B was adopted in the Cyrillic alphabet.