Obviously the electoral system contributes, but it's mostly a reflection of Israeli society which is remarkably fragmented and multi-polarised.
Yeah, this. Even beyond the obviously exclusive groups (Hasidim, Arabs), the vast majority of people living in Israel had virtually nothing in common 100 or even 50 years ago. A Jew in Moscow, a Jew from Brooklyn, and a Jew from Yemen lived totally different lives prior to the founding of Israel, then they were quickly thrown together for mostly political reasons. Of course that's going to cause a fragmented society (and thus fragmented elections).
The Israeli Labour Party led by Eastern Europeans - mainly Poles, where quite succesful in integrating various groups under one umbrella in the first four decades of Israels existence and from the 70s onwards Likud managed to unite the right wing. Allowing the party system to fragment based on the various religious and ethnic cleavages was very much a result of the electoral system - and especially the low threshold.
The fragmentation started in the 90s. As late as 1992 Labour got 44, Likud 32 and Meretz 12 of the 120 seats. So almost 3/4 of the seats to the three largest parties.