The ground wire should be properly connected back to the box ground connection, or back to the line ground if there is no ground connection in the box.
Some will argue that the metal screws provide the grounding to the plate and so the ground wire is superfluous.
However, there are two issues with that.
The screws and the screw holes are very loose tolerance. The screws wobble around in them. The plate itself gets painted over, OFTEN. Any paint or other contaminant, eg. drywall dust, can get into the screw threads and break that electrical contact quite easily. That leaves your plate ungrounded.
When working on the switches, it is not uncommon to have them hanging out of the box while the electrician, or would be electrician / E.R. bait, works on the circuit as a whole. If you do not connect the ground wire, the plate again is, obviously, ungrounded.
The code in your area may indicate it is not necessary, so not doing so may be legally "valid", but for complete safety, you should wire it up anyway.
BTW: Inspectors do not inspect every outlet, that would take too long. Instead they normally sample test a few and trust that the electrician followed the same standards everywhere. The electrician, not knowing which outlets the inspector is going to test, is therefore "enticed" to do them all the same way.