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@moth
You understand that fatter = stiffer, assuming the same amount of metal? (It's simple geometry - because the fat tube's metal is further from the tube's axis, it has to move (stretch, compress or shear) more for the same angle of twist or bend.)
So you are really asking 'why bother tapering the ends of the fat tube?'
I think the answer is: tubes are tapered where other things are more important than stiffness.
As you go down the forks, stiffness gets less important because there is less tube left to waggle, but when you get to the dropout you want to make a joint that transfers force evenly to the tube. That's easier if the tube diameter is smaller.
Chainstays taper because near the bb they are acting more as beams (stiffness of structure depends on stiffness of tubes & joints), but where they meet the seatstays and axle the structure looks more like a truss (stiffness of structure just depends on lengthwise elasticity of tubes).