The biggest advantage of a chest protector is in the reduced risk of breaking your collar bone. If you think about a common crash, it is common that your chin tucks towards your chest. Now, since most of us wear full face helmets, as the chin tucks towards the chest, and we land on our head, the helmet is moved to one side or the other. The bottom edge of our full face helmet contacts our collar bone, and SNAP

, the collar bone is broken at the point of contact. We then get to wear one of those cool braces that pulls our sholders back and pushes our chest out.
This is not to say that collar bones can not be broken while wearing a chest protector, but it is certainly more difficult. In a crash, instead of the bottom edge of the full face helmet contacting the collar bone, it contacts the plastic chest protector and spreads the impact over the entire length of the collar bone and shoulder, eliminating one small point of effect on the collar bone.
While we have had our share of stitches (my wife does not even consider stitches real injuries anymore) and a few broken bones, in all the years of riding (and crashing), we have never had a collar bone injury.
In short, purchase a good, comfortable, properly fit chest protector for all the riders in the stable.
Rick