Best L/D is well above stall speed. 1.3 minimum of stall speed rings a bell. Max lift occures right before stall but the drag is at max. That is why low altitude stall recoveries sometimes have to sacrifice speed for more lift to not impact the ground. Best L/D is close to best glide speed. It is best to not venture below this speed but some situations require it. The shaker is a warning you are approaching stall angle of attack but if you don't force it to go deeper into the stall you have almost max lift but also almost max drag. Breaking out at 500 ft getting a stick shaker and lowering the nose first would only compound your situation. High sink rate and low speed is not good. Add power to recover and minimize sink rate.
It has worked well for 107 years.