Yes, you can move clubs into the "unassigned" bin, but it won't let you delete a club that has been used, so everything added to the "my bag" stays there. The system used to let you delete a club but would give a disclaimer message saying something like deleting this club will also delete all of the data associated with it.
What is annoying about this is that in post-round editing, all of the clubs, assigned or not come up in editor. So if a shot was registered with the wrong club, it's not intuitive to pick from the list which is color coded rather than providing a description. This is rare - it would happen in cases where you put a new club in the bag but didn't update the "my bag" section so shots were registered on the old club. Or possibly a scenario where you took some practice swings with a 8-iron and it registered a shot, but then you actually hit the shot with a 9-iron. For example, below, this is what I see if I wanted to change the driver I used for this tee shot:
That is the course we staid on when we did our golf trip to Orlando like 8 years ago. I really like that course. Fair, but you really have to figure out how to play it due to the amount of bunkers on the course.