The aircraft are certified under these conditions - 1 second delay for civil and 2 second delay for military.
Of course students are quick - they know it is coming.
You guys need to stop deluding yourselves about your reaction time to an engine failure when you are busy flying and trying to complete a task.
The first thing you will probably notice is a change in noise, long before your brain has started to process loss of Nr - even though it is happening quickly from the point of failure.
You might react automatically to a slight reduction in height - especially at low level where your cues are very good - and will probably react by raising the lever because you haven't realised why you are descending - there goes some more Nr.
By the time you actually diagnose the failure and react to it, the Nr is decaying rapidly and you are already moving further from the point where you can make a safe EOL. Any flare might help to recover the Nr but it isn't going to stop you descending unless you are plus of about 100 kts.
If you are very low level, your flare may well smack the tail in - adding to your problems.
It really isn't rocket science.