I remember being constantly reminded of this by several teachers as a child. I just thought of it as an annoying little thing that I had to keep in check to avoid being chastised in class. Thankfully the positive habit stuck and I never had to think about the reasons for its importance until I myself became a teacher.
Unfortunately very few teachers bother with explanations to justify this rule of thumb (sorry, I had to). I myself only began to see it's value when I had to come back to the basics of bow hold with my students much later.
With self analysis and slow practice (especially in difficult technical passages), I began to notice that tension starts accumulating at the base of the thumb and is released only when I unlock the thumb from a fixed position and move it back into a natural curved posture. This requires mindfulness and constant self diagnosis, qualities that rarely found in young children. All of a sudden the constant reminding from my teachers made sense.
The thumb is attached to the palm with the biggest muscle in the hand while other fingers are primarily controlled by tendons and ligaments that stretch up into the forearm. If left unchecked, tension is allowed to build up and a straight thumb locks it in. This alone is the underlying cause of multiple of problems resulting in poor sound, lack of fine bow control and even injury. This logic extends to the left hand thumb as well and will be covered in a separate post.
When encountering real difficulty in instrumental playing, our first instinct is to tense up, leading to muscles contracting into an unnatural position. The natural (default) position of all fingers is gently curved and it is important to maintain this regardless of other difficulties. This may be difficult at first but a little mindfulness during practice goes a long way to improving awareness and control.