What is the purpose of hook turns?

You are correct. In Victoria, for reasons that are lost in the mists of time, originally every right turn was a hook turn.

In the mid 1950s this was changed to the 'diamond' turn, and diamonds were painted at vast expense on practically every major and minor suburban intersection to train us. I remember this well.

Diagram of a diamond turn

However, originally all intersections where trams cross were exempted from this, and this was later restricted further to just five City intersections: Swanston with Flinders, Collins, and Bourke, and Elizabeth with Collins and Bourke. These were left as hook-turns to facilitate trams. Some time in the late 1990s this was 're'-extended to most of the City intersections involving trams.

The basic idea is to clear the trams before the right-turners. If you're already camped across the tram-tracks waiting to do a right-hand turn, it is not legal for another vehicle, say a tram, to enter the intersection until there is room for it on the other side, which might never happen given that cars can accelerate into that position faster than trams can.

The key point, that isn't exactly obvious in the description, is the vehicles waiting to turn are waiting outside the traffic flow. Meaning, they have essentially pulled over while waiting to turn while forward traffic continues.

They then execute the turn during the signal change after oncoming traffic has stopped.

This is essentially similar to many US States where it is legal and expected to wait to make a left turn inside the intersection. The major physical difference being the turn lane is between the travel lanes.

Very simply, its so the turning vehicle does not block continuing traffic.

This would be better as a comment but I haven't earned comment rights on this SE yet :-) There's a second definition of hook turn which I encountered when learning to drive in New Zealand (and again 30 years later when getting my HT and passenger licenses): On a single carriageway high-speed road (e.g. a rural highway) a hook turn may be used to safely turn across the opposing traffic lane into a side road or vehicle entry. E.g. (driving on the left) - if there is oncoming or following traffic I would pull over to the left shoulder just before the turn point and indicate to the right, waiting until the traffic has passed before completing the turn. This avoids you being stationary in the traffic lane. There are wider shoulders at many rural intersections to allow for this. I have found that in practice, driving a school bus, it sometimes doesn't work - following traffic has come to a halt behind me instead of passing. I blame this on American video games where it is illegal to pass any school bus.

However, on researching, I found that the type of hook turn described in the wikipedia article linked above has recently been introduced in New Zealand.

The reason is 'trams'. Right turn movements requiring dedicated phases/filter turns tend to delay tram throughput. By having hook turns, intersection can simply be managed in two simple phases increasing efficient for trams.