This doesn't sound like a man that had no interest in being a Captain.
Takei wanted to play interesting and challenging scenes
, not necessarily that his character got promotions. After all, Sulu was promoted for TMP and ST II, and his lines stayed the same.
"Glorious! I worked hard on that one. I lobbied and lobbied and lobbied. Finally it happened"
He lobbied at conventions
for a TV series spin-off called "Captain Sulu", he wasn't demanding it of the studio for ST VI.