As Karen Tuttle always believed, playing with good coordination is paramount. Galamian had another way of saying the same thing: “'Right’ is only what is natural for the particular student, for only what is natural is comfortable and efficient.”
With these insights, the answer to this ne'er-ending question changes person by person. However, there are useful trends to consider when making your own choices about instrument setup.
However, upward tension of the shoulder, downward pressure from the jaw (which should make contact with the chinrest), or craning of the neck should never support the weight of the instrument in compensation. Thus, many violists, given that they play a heavier instrument, use a shoulder rest to more evenly distribute the weight. Yuri Bashmet below is one fine example (Michelle LaCourse, and Lawrence Dutton also do, just to give some others).
Often, the player exhibits similar setup to the teacher, so exceptions do occur all over. For example, Primrose, who played in the Russian style, also didn't use a shoulder rest as that was not practice. Zukerman, who is originally a violinist (a student of Galamian), plays with no rest as he was trained, even on the viola, perhaps supporting the instrument in his hand more than one with a shoulder rest would. The issue of supporting the instrument with the hand is really more of a left hand technique consideration, and even today is a rather rare find.
All in all, as my teacher says, "bring the instrument to you, not you to the instrument". If that means you have a short neck, perhaps no pad is needed, but if your neck is quite long, consider your support options (sounds like I'm talking about counseling!).