I've created an improvement for the Block Course List. See attached images. Ignore the attached files as I've got them on my github now.

I've made it possible to show the shortname and categories.

As far as categories go you can just show the top level or subcategories.

There is a little issue of hidden categories and how to handle that. There is an option of showing the names regardless of the users role otherwise it will just display dashes - to keep the hierarchy. Not a big deal when showing just top level but the subcategories is a little messed up. Maybe either omit this from possible integration or rework it. Regardless if you have chosen subcategories then you shouldn't be hiding them.

Hopefully the changes I've made are reasonable and can be put to good use as I've been getting lots of complaints from my institution about being able to do this.