Well, thorn came into the language more or less at the dawn of the English scribal tradition (i.e., the late 7th and early 8th century), and is a direct scribal representation of the runic (futhorc) character of the same name. Eth, on the other hand, is a Romanisation, and its popularity develops over the course of the eighth century. Once both established themselves, their simultaneous use is indeed superfluous, but largely persisted for the next six hundred years, being very much entrenched for the duration of Old English. Again, thorn is the longer lived at the end of their era, having persisted into the latest stages of Middle English (in the late 14th century). But ultimately, what French influences had been insufficient to fully accomplish, the printing press (whose type contained no such character in any other literary language of the region) would do once and for all. Before the English vernacular had managed to undertake its great literary resurgence of the Early Modern era, thorn had been done away with (and earlier and more completely, eth as well).