Tomaski,
You've hit the proverbial nail right on the head. I think in all recurrent simulator training routines there should be at least two totally unexpected failures. It is not difficult to have a selection of such failures that the instructor can throw in at random, and to do so totally unexpectedly, so that the pilots are startled. It need not be done in the competency details when the pilots are under check but in the refresher/training type details, and with helpful debriefs afterwards. Think how often an engine is failed shortly after V1 when the pilot is half expecting it. For example, what about failing it half way through the flap retraction? Or on the approach when turning onto the ILS? And how about a TCAS when in the hold? Or some subtle instrument failures at a time of busy workload.
I have never flown the modern highly automated aircraft, but I am sure those who are familiar with them can think up some suitable problems which will suddenly dump the flying in the pilot's lap when he/she is least expecting it.
The main thing is not to use such failures as 'gotchas' but rather as a means of showing how confusing a startle can be.