If you have a dedicated circuit, you can send dummy data 24/7 to mitigate any traffic analysis. Even if you don't, you configure each link to send dummy data, so eavesdroppers can't do any traffic analysis without compromising the node itself.
Traffic analysis tells your adversaries who you communicate with, and what apps you're using, inferring what communication was caused by what preceding communication, etc which lets your adversary guess what the communication was about. Esp when compared against what other people is communicating about just then.
Yes, which makes it a particularly bad idea to run unencrypted metadata over satellite connections if it can be avoided – and that's the case for communication between data centers, arguably.
That might change once lasers or extremely tight radio beams can be used for ground stations, but for the latter you'd still need to make sure that nobody can get reasonably close to your ground stations, which might be possible for remote military bases, but probably not for AWS data centers.
