Brakelights don't mean the handbrake isn't engaged, just that the footbrake is engaged. It's not an 'either/or' choice.
Many modern automatics (like mine) disengage the drive when the footbrake is on, but not when the handbrake is on. Whilst I put the hand(actually, foot operated)parking brake on if stopped for any length of time (such as at lights which are not likely to change within seconds), I'll often keep the footbrake on. First it is always on until I have a vehicle stationary behind me (i.e. let them see those big red lights to reinforce the fact that I'm stopped), second if I'm at the front of the queue, engaging 'parked' means that to move off, I have to (i) engage foot brake (ii) engage forward drive (iii) disengage parking brake. At the front of an impatient traffic queue the time taken can irritate others. Further back in the queue, the time is not an issue (as long as I can see what is going on ahead), so I'm more likely to be able to come off the footbrake.
Edit: Hearsay, but I was told by one advanced instructor that automatics suffer fewer rear-end shunts; the suggestion was that they tend to have brake-lights on more often when stationary, even if the handbrake was on.