Why did the Flavians build their Amphitheater?

In this two-part look into the evoluation of the Flavian Amphitheater, I left out one big issue that I hope we can discuss.

Why did they built it?

Easy answer is that they wanted to show their power and firm up their rulership. But couldn't they have achieved that with another type of building or even multiple buildings?

I want to learn why you think they built this structure so please a comment and let's start talking!