The reason to keep the mooring bridle attached to the mooring is one of great convenience, simplicity and to save serious grief as follows:
The rising chain from the ground to the main (mine) mooring buoy (which basically always stays in the water) is very heavy ie to take 12 tons, to which to ensure good holding for the boat the bridle must be attached underneath the main mooring buoy to the top of the riser chain.
As you probably know that also attached to the main mooring buoy (again underneath to the riser chain) is a pick up buoy which would either have a length of heavy chain (in normal circumstances) attached to it or in my case the other ends of the bridle which can be easily attached/detached to fix to the hulls when mooring or departing.
If the bridle was attached to the boat it would mean each time I moored I would have to get into the dinghy
after having picked up the pick up buoy and made fast temporarily, and attempt to make fast the bridle to the top of the riser under water
and then the reverse procedure for when leaving the mooring, hence why the mooring bridle be attached to the buoy.
I know that there are buoys with rods going through the middle but the safest and strongest way is (as far as I am concerned) is the way above.
bridle is a different matter - this would be attached to the boat at all times.