Kind of a big deal if you can't host that MP4 somewhere? If Google/Twitter/Facebook/etc. don't want your stuff ... chances are Amazon doesn't want to host it either. Even if you stand up your own hardware, you're at the mercy of whatever company is providing you the internet connection.
Free speech as a principle isn't about hearing stuff you like. It's about hearing stuff you don't like. That's where the tolerance part of it comes in. When you're tolerating something, it means you're putting up with it even if you don't like it.
And it's not about the law. Yeah, they can do whatever they want since they're private entities. It's about what values we choose to uphold as a society.