Because sometimes it's necessary and providing you are sensible about it and take the appropriate precautions it can be done quite safely with minimal risk.
Before I start poking around in a live board, I always give it good look through and after that, if I can do what I want to do safely with minimal risk I proceed. If not, I ask the customer if I can turn it all off... if I can, groovey, if not I enquire when I can and potentially schedule a mutually convenient time for the work to be carried out.
The old Wylex BS 3036 boards I'm not keen on working on live because of the abundance of bare metal and close proximity of some of those exposed conductive parts (but even after turning off the main switch, there is still a significant risk).
I have had some close calls where idiots have damaged the incoming tails leaving the bare conductor exposed at the rear, thankfully had a good look before I stuck my fingers in there but you can't so readily turn them off, so what do you do in that kind of situation?