Boxing teaches you to deal with punches to the head a vital skill for self defence. The other spin off is fitness. You can beat a good Boxing coach for excellent instruction andwith a good gym you will meet and train with some great un pretenous individuals. I have never loooked back.
This. I can't even begin to say how many times I've seen people freak out over a fist coming at them. If you learn how to deal with the threat of being punched in the face then you've got a HUGE leg-up on most of the idiots out there. Other than that I have to ask why, if your hands are already your strongest point, you would feel you need even more training? I'm the opposite I feel like because my kicks and lower body techniques suck I should be focusing on them all the harder.
Boxing can be a useful skillset for your self defense tool box as long as you understand the psychological, verbal and emotional aspects of what is involved in a violent and sudden attack. Go for it. Just remember to understand the above mentioned elements.
Boxing is great for SD. Most guys do not know how to punch "properly", nor do they know the proper way to defend against a punch. Fortunately, I have never needed to use boxing for SD, but I have the confidence to do so if needed. Give it a try. Not to mention, it is great exercise.