I get your point. But it makes it complicated to make some ripple shots with Hellfires (especially RF ones) for example.
IMO, the best would be to still have the list available after the right short command + consent fire. And in the case of a target moving away the field of view, just removing it from the list.
What I miss the most, it's be to be able to switch weapons after the list appeared. Because for example, if you are running with guns, you ask George for targets, a heavy tank appears and you want to engage it, you need to restart the process... (except if I am missing something?)