I am aware of (and have examined) a number of inscriptions dating from that period, most notably the Davidic inscription at Dan in northern Galilee. (I left Israel prior to 2008)
The Elah text certainly does not "prove" that there is no writing prior to that particular find. It is merely the earliest extant example of Israelite writing that has been found to date.
Indeed, it would be folly to claim that no prior writing exists, as further excavations are likely to reveal earlier examples. Only a tiny fraction of the archaeological sites in Israel and the Middle East have been excavated (and those which have been excavated have only been partially excavated).
Indeed, the whole theory of the Israelites existing for centuries without writing is based on a largely discredited 19th century German theory known as the Graf-Wellhausen Hypothesis. This "Documentary Hypothesis" was taught years ago as unquestioned truth, but in reality the hypothesis has split into many squabbling factions as archaeological evidence renders it increasingly untenable.
BTW Wellhausen's original Documentary Hypothesis held that there was no Israelite writing prior to the sixth century BC. - much later than the theory to which you are referring.