Greater performance means just that whether you're on one or two engines. And having a greater initial climb rate means that you will have MORE altitude. All achieved by this ever so dangerous 21 degrees of pitch.
Given that this apollo rocket type departure is only going to happen up to the flap retraction altitude, which is every airport I've flown a jet into lies between 1000' & 3000' agl., why would you be interested in maximising the initial climb gradient to such an enormous extent for only a few seconds? If you did this out of some places with SID at 3000' and arriving a/c down to 4000' I'd expect to get an RA passing 1000'. It seems like making an relaxed departure into the opposite. Why oh Why?
I think we've reached the time to say "let's agree to disagree." This could keep going round in circles for ever and use up all that potential energy when I'd rather had some kinetic.