Off the top of my head, I can think of a couple of reasons...
If I'm OOA, my regulators is obviously useless and I want to be able to easily put in a working reg into my mouth.
If my buddy is OOA, or some say OOG, I want them to take the working reg out of my mouth and I'll switch to my back up.
If my primary reg free flows or malfunctions, I want to be able to switch to my secondary.
If I want to blow or shoot a bag to the surface, I usually use my primary reg because it is on a long hose.
If I want to switch to a different gas, I need to switch regs.
If I want to talk to my buddy on the surface before or after the dive, I need to remove my reg.
Nearly any medical situation underwater isn't good. If you look on DAN, a lot of diver deaths are attributed to drowning, but what is not a clear is what caused the person to drown, i.e. heart attack.
They say SCUBA is the great equalizer and that nearly anybody can do it. They are correct, but I disagree. If you require a XXXXL wetsuit, maybe you should rethink your lifestyle before diving. If you smoke a pack a day, again rethink your lifestyle.
Last Sunday I dove for the first time with doubles. My rig alone was easily 90+ pounds. With my exposure protection and the 100+ yard walk to the water, I had to float and relax for a moment, and cool down, before the dive. Odd to say when your dive profile ended up being Max Depth of 75ffw, Ave Depth 43ffw, Temp 46, and Dive Time 52 minutes. My SAC wasn't great, it was .74cuft/min. It was a stressful dive.
There are full face mask out there that technical divers will use, that will allow them to switch regs. I've never seen one in the wild, but they do exist.