In EoE, Yui was clearly in charge. Shinji was synchronized to the point that he got visuals and felt Eva's pain, but he really had no say over anything that happened (except condemning all life on Earth to liquidation).
This was NOT a standard launch procedure, wherein the umbilical cable would be attached and restraints removed, blah blah blah. Yui basically broke out of the Cage, blasted the Pyramid to hell, sprouted wings, and levitated up and out.
The #23 instance makes perfect sense for the reasons I stated before:
(A) Nerv didn't want to fuck around with the S2 (or else risk getting wiped off the planet like EVA-04 and Second Branch)
(B) Yui took the S2 in for her own purposes, so it figures that she'd be the only one who could use it.
#24 poses a problem, though... We see both Evas active for over five minutes (without the pylon battery backs).
The fight scene in the shaft also confuses me -- aren't they both basically in a prolonged free-fall? Seems awfully controlled, for such...