What is the purpose of a movable inlet on a jet engine?
Jet engines require the air that flows into them to be subsonic. Supersonic air hitting the front fan would cause shockwaves inside the engine, with undesirable results.
So the job of the intake on a supersonic aircraft is to slow down the air to subsonic speeds. The intake is designed to set up a series of shock waves. The air will slow down to subsonic speed as it crosses these shockwaves.
The location of these shockwaves changes with speed: the higher the speed, the shallower the angle of the shockwave and the further the shockwave will reach down the intake duct. So if you have a fixed-geometry inlet, your maximum speed is limited: there is a speed at which the shockwaves will intersect the front fan.
Variable intakes avoid this problem: the movable vanes in the inlet aim the shockwave so it stays in front of the front fan at all speeds. This enable a higher top speed to be reached.
If you accept a lower top speed, you can avoid the extra complexity of a variable inlet. For the F-22, for example, a variable inlet would make it more difficult to maintain a low radar cross section, so the tradeoff was made to maintain stealth and lower the top speed.