Why is the inheritance of acquired characteristics thought to be rare?

Because it has been demonstrated many times that LaMarck's "Inheritance of Acquired Characteristics" (1809) is wrong, and that characteristics acquired during an organism's lifetime are not passed to offspring. Therefore, variations that are necessary for Natural Selection to drive evolution must be passed on genetically.

I don't think it ever occurs. Acquired means you have received the trait in your lifetime, like the ability to do some action, and evolution is based on your genes, passing them onto the next generation. Jean LaMarck thought acquired traits got passed on, like giraffes stretching their necks in their life time to get food, and therefore leading to longer necks in their offspring. But, evolution says there were giraffes with long and short necks based on their genes, and those that had longer necks could reach the food, survive and reproduce, which is evolution.