Why not? The most lawspeakers are of one of the noble families there. In Iceland there are some nobles families, which fight for the power. The Gothis are de facto hereditary priests. There are six families. Haukdælir, Oddaverjar, Ásbirningar, Vatnsfirðingar, Svínfellingar and Sturlungar. This sound for me more like a monarchy, then a republic.
So I would vote for electiv succesion instead of a republic with a random ruler.