Things certainly appear to have changed since I trained and later instructed on the JP. I certainly have no recollection of being taught, or instructing, to try a relight following a low level flameout just after take off, no time. How long does it take to get a failed or flamed out engine up to idle and then accelerate it to useful, questionably reliable, thrust? Too long, I would suggest, and all the time you are compromising the safety of an ejection. Can one depend on an engine which has just failed, for whatever reason?
Zoom and boom following EFATO at low level as in the Snowbird accident, certainly looks to me, 57 years after my ejection, to offer the most likely safe outcome.
Even now, if the engine failed in my Warrior and I set it up for a forced landing but I can restart the engine, I would probably continue with the forced landing if it was looking good. If the engine WERE to restart but then failed again after throwing the forced landing away. it the may well have compromised a successful forced landing.
A jet with an ejection seat is not dissimilar in that after a failed or partial restart one may be faced with a low level ejection from a descending aircraft. Valuable height wasted, perhaps taking you out of safe ejection parameters. .