Having flown in old jet aircraft without zero zero ejection capability (Vampire, Sea Venom and Macchi MB326H) it was certainly of some 'comfort' to know the A4G Skyhawk rocket powered zero zero seat was available. For two A4G pilots aboard HMAS Melbourne the seat worked well during a cold cat and an arrestor wire failure resulting in successful ejections. Another pilot ejected OK not far from the ship still at deck height after the engine failed just after catapulting.
"IF IN DOUBT - PUNCH OUT" was burnt into our brains with "out of control below 10,000 feet - EJECT" another mantra. However this last one had many provisos - according to what 'out of control' meant at the time.
As the other posters state above, the auto eject function seems to me to be a good function in the circumstances described, with the STOVL function actuated some distance from the ship usually; BUT engine failure can occur anywhere at any time.