Why are inlet vanes used instead of variable geometry inlets to prevent compressor surge/stall?
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.