Why are inlet vanes used instead of variable geometry inlets to prevent compressor surge/stall? Jet engine core axial compressors (that of subsonic turbofans anyway) are designed to keep air flowing the right way at max RPM(or close to it). Below that, the airflow slows more and more, and becomes unstable.
In other words, the compressor can no longer compress the large air volume flowing into it. To prevent this, variable inlet vanes are used to reduce the airflow volume into the compressor at low RPM. 

My question is: why was this method chosen? When you're running the engine at low power/RPM, the closed vanes will create drag by presenting their blunt face to the air. So why not use a streamlined variable geometry inlet which can forespill the excess air with less drag? such as the following:



TOP: low RPM, a sliding annular door narrows the annular gap

BOTTOM: high RPM, the door slides back, widening the annular gap
What you propose is used as a dust filter for helicopter engines, but even there the plug is not variable. Instead, air spills over the rounded edges of the intake if less is needed.

Intake vanes never close to a point where they would block the intake; instead, they direct the flow such that it hits the compressor blades at the desired angle of attack. They can be moveable to adjust flow to a range of compressor speeds but they never block the flow. Flow control is simply achieved by pumping more or less air into the compressor by means of varying compressor speed. If less air is pumped, more ram pressure builds up in the intake and forces more air to spill over the intake lips. If no separation occurs, this causes little drag and is preferred over something that adds more mass and complexity.

A variable intake body similar to what you propose is only used on supersonic intakes when the shock originating from the tip of such a spike needs to be positioned close to the intake lips in order to achieve uniform flow conditions at the intake face and high precompression efficiency.