I can only speak in theory as I haven't had the pleasure of a conical myself.
Removing lees... After lees settle to the bottom a valve is opened to allow the lees to be removed with out transfering the entire batch. When the outflow clears, you close the valve.
Connical bottom would concentrate more of the yeast in the center, making more of the fermentation in the center, creating in essence an up draft in the center of the tank... possibly this would increase agitation and better stir the must, as opposed to a diffuse bubbling.
Cleaning, All the water will run down and out the center whole because it is the lowest point. Compare this to a jar used for sun brewed tea with a spout on the side... water level drops below spout, you have to tip the 1 gallon Jar to get rest out... Now imagine a 500 gallon jar of Stainless Steel.
They used to have a plastic Connical in Homebrew size, But i never got my hands on one.