Is there a reason to put a product in both the Child and Parent Categories?

Most of my Woocommerce clients only have the child category checked, not the parent.

For instance, this structure is the most widely used when you have subcategories:

[ ] Clothing
    [ ] Pants
    [ ] Shirts
[ ] Music
    [X] Rock
    [ ] Classical

The single product page would show this for the product categories:

Categories: Rock

But if you chose to check both the parent and child category, like this:

[ ] Clothing
    [ ] Pants
    [X] Shirts
[X] Music
    [X] Rock
    [ ] Classical

The single product page would show this for the product categories:

Categories: Music, Rock

But as per usual, it depends on your theme and any plugins that may deal with category archives. The main thing to remember is that when you browse category archives, all child categories are shown.