In my opinion, the punishment doesn't fit the crime. A simple warning, written or otherwise would have sufficed. With regards to your own habit of being late,

In my opinion, the punishment doesn't fit the crime. A simple warning, written or otherwise would have sufficed. With regards to your own habit of being late, to echo what others here have said, it is something that you should fix. At one point I fell in to a pattern and I was constantly late for everything, it took a concerted effort to fix it and I think it was quite necessary. Generally, being late is seen as disrespectful and an inability to keep your word. I've had people in my life at certain points who would show up up to 20-30 minutes late for some events. At that point I was too rattled by their tardiness to even want to interact with them. I am sure the same can be said about others towards me when I fell into a habit of being slightly late for everything. Take yourself out of the equation and think about how your behavior makes others perceive you.