The earliest sources, from the fourth century, indicate that the anaphora was a central part of the liturgy.
But the advent of large cathedral churches -- especially ones with patriarchal and imperial retinues -- necessarily changed/shaped liturgical practices. According to St. Maximos the Confessor, the anaphora was recited "mystikos" (silently/quietly, i.e. not chanted aloud) during his time. Obviously, in a huge church like Hagia Sophia with thousands of clamoring bodies, simply reading something in the altar would not be audible to the hoi polloi. So, from at least the sixth century, the anaphora was "silent." The earliest "rubrics" we have, from the ninth century, also call for "silent" prayers. Eventually, this produced a whole theology of "mystery," complemented by a high iconostasis, closing the Beautiful Gates and extended chanting, so as to fill the silence. Such was the case in most locales for many centuries (except maybe in churches built by the Venetians). That's how they do it on Mt. Athos and every parish I've been to in Greece, Ukraine, Bulgaria & Romania.
With the advent of modern liturgical scholarship in the 50s and 60s, and the discovery of this history, some parishes have started to read everything aloud, for all to hear. In North America, SVS has been the main force behind the movement, which usually goes hand-and-hand with Schmemannite Eucharistic theology.