You're right, Decker was clearly visually identified as a captain when we first meet him, although I still think my theory is right that "the price" Kirk must pay for wanting his old ship back (and everything we know about in the Phase II series format documents assumes that Kirk is indeed a captain for the majority of the episodes, not an admiral-acting-as-captain) is a permanent reduction in rank and being stripped of the assumed privileges thereof.
I agree with this and don't believe Kirk would've been allowed to command Enterprise
again without making significant concessions. The conversation between Kirk and Nogura is something I've always wanted to see or read. If their meeting did last only three minutes, one wonders exactly what was said between the two if Kirk came out on top.
Of course, we must further assume that if Kirk did command a second five year mission between TMP and TWOK, and the ending of TMP certainly implies this, then his 'permanent' reduction to captain for a further five years was in itself only temporary, and a loophole was used to bump him back to admiral upon his second return to Earth.
Several non-cannon sources suggest that the admiralty was reorganized in the years leading up to TWOK because of several mistakes by Starfleet Intelligence, including a botched mission in Klingon space. Nogura was asked to resign, with Morrow taking his place. Kirk was returned to the admiralty and placed in charge of Starfleet Academy. Eventually, Enterprise
was placed under Spock's command and assigned to the Academy. Whether this was a move engineered by Kirk to keep the Enterprise
within his jurisdiction or something Spock requested so that he could continue to serve under Kirk isn't known.