Although the CFM 56 is one of the most reliable engines around the point you raise is a fair one. I personally always fly around with this screen displayed. It just improves my situational awareness in the larger sense of the word...and as you say there is no real reason not to.If something big breaks the displays will rapidly start changing colour etc...so it is not like you are going to miss it if just because it doesn't "pop up".
The engine itself has an an historical in flight shutdown (IFSD) rate of 0.001 / 1,000 flying hours. If you were to fly 30,000 hours in your flying career then you have a 6% chance of an IFSD.
Can't give a split of instataneous vs gradual run downs but a lot of IFSDs are due to loss of oil. Loss of oil will result in a catastrophic failure of your engine and the only place where oil temp / pressure / quantity is displayed is on this screen.
A quick internet search brings up the V HTJX incident where for one hour a significant change in vibration on one engine was not spotted by the crew before it ultimately failed.