We have essentially this same need. In our case our learners self-enroll from the catalog on the home page, so it is just My Courses that is a problem. We also do not un-enroll learners - they are allowed to un-enroll themselves, but this almost never happens in practice, and the assumption is that they may want to return to the course even after completion as a reference and/or to print a completion certificate.
From a learner point of view, they want to see a list of the courses they have enrolled in with either an indication on each they have completed the course (and sortable by completion status), or separate lists of completed and not-completed. Ideally within these 2 courses would also be sorted in an order that makes sense to the end user, not by category, which mostly makes sense to the administrator - a simple alphabetic sort would make sense.
Currently, I am looking at ways to get at least some of what we are looking for though other plugins, but ideally this would be a direct replacement for the Courses Overview list. The fact that we are offering completely self-directed learning often makes plugins a mismatch - for instance I would love to have a Learning Plan plugin, but not for Admin/Manager/Teach to create the plan, rather for individual learners to create and manage their learning.