I was reorganizing my Trello when I ran into this edge case that I feel should be addressed. When I added a ninth and final label, this apparently made the "Show More Labels" function kick in, which resulted in this behaviour:
Effectively, the "Show More Labels" button hides exactly one label, which is the same height as the button itself. It adds an extra click to no benefit to the UI or UX and, to be quite blunt, is less than useless in this specific situation.
My suggestion is to display up to 9 labels, and have it hide 2 labels when a 10th one is added.
To cover all bases, if these values are different depending on the size of the viewport, app, or whatever else, then have it display n+1 labels, and hide 2 labels when an n+2nd one is added, where n is the current display limit of the viewport in question.
Alternatively, just add a scrollbar. It works just fine for cards, why not labels too?