Why is the Formula for F1-Score Unnecessarily Complicated?

Why is the Formula for F1-Score Unnecessarily Complicated?

What's up with this formula looking so crazy? Visuals Created with Excalidraw: https://excalidraw.com/ 0:00 Motivation 0:46 Additive Approach 4:22 Multiplicative Approach 6:10 Harmonic Approach