The question follows: are there any benefits to using fingers other
than one's index when playing pizzicato?
When playing right hand pizzicato you have a choice. When playing left hand pizzicato you have less choice.
Here is a video on left hand pizzicato by violinist Vivien Hoffmann which makes some useful points. As she says in first position it is easier to pluck the open string with the fourth finger of the left hand than the first because the angle is better and the string is higher above the fingerboard. If the finger is held down then it is impossible to pluck the string with the first finger of the left hand.
Hoffman also makes a point which is relevant to right hand pizzicato when she warns against practising pizzicato for more than very short periods of time because of the danger of developing blisters on the fingers.
In the piece in the question Perlman plays three consecutive notes with right hand pizzicato. During practice if he always used the same finger then he would be much more likely to develop a blister on that finger. By using different fingers for each of the three notes he reduces the risk and extends the amount of time he can spend practising that section. In performance it then makes sense to play what you practice.