This is true, but I'm not going to pretend I care. Sorry.But it didn't have to be the ISS Enterprise.
It was the ISS Enterprise because they wanted to have a scene where Burnham talked about her foster-brother. That's what the scene is really about. It wasn't about the ISS Enterprise. It was about Burnham thinking of her brother. Let's not pretend that wasn't what it was meant to be about.
Plus, I'm agreeing with other people who say they're going to give that ship a 32nd Century makeover... and finally answer the question anyone who's a Trekkie has been wondering (secretly or otherwise): What letter are they up to now? Anyone who says they're not even remotely curious about that is lying. It's going to come up eventually.