I had, in fact, searched for beam view, beam camera, and beam cam, and none came up with any results, thus making your suggestion of using search just a pointless waste of time and effort. Shock shock, I'm not stupid.
As for reason for it, sometimes if they're far away, it's hard to tell if you've passed them or not, and so far I haven't found a way to turn the beam back around without actually turning yourself around, meaning you have to move your target out of view.