> Things leave your field a view much faster than anticipated.
Not sure about that. NASA has been using Kineto Tracking Mounts and ROTI (radar-assisted and optical tracking) since 1981. Those systems were developed for the Columbia launch. I find it hard to believe that today's computer-guided cameras would let anything slip out of frame unintentionally.
Those cameras are for official NASA archives and study of the launch. Those are not for some webcast live stream. Maybe they can piggy back a live stream camera to it for the next one, but they are not going to dedicate one of those mounts for a live stream camera, and I doubt they'd allow for a tap out of the feed.