I'd assumed that the Echo is only communicating with the hub, and the hub is what's telling the remote the current status. So, it's probably more correct to say the hub is hanging trying to turn on the xbox, and the remote is just reflecting what's going on with the hub.
I wonder if this has anything to do with how I have to put my XBone into "completely turned off" mode rather than sleep?
Though, come to think of it, you'd think that would affect normal operation then and it doesn't. Works just fine if I use the remote or the mobile app to turn on the XBox, it's only over the Echo that I have an issue.