no clue why he isn't. maybe he is just afraid of the other captains, or he just doesn't want it. i have no clue how the anime creators think so.

lol...lemme see...i think i know why none of the captains would approve of him

Soi Fon: 2 hit kill him, fast enuf to dodge Zabimaru

Unohana: >.> would just use the healing thing, or have hanatarou fight for her

Kenpachi: No way in heck that guy would approve renji

Byakuya: Still owns renji

That's four so far, and with only 10 captains around...

Hitsugaya: Doubts renji could beat him

Mayuri: Would use cheap tricks to kick his rear >.>

>.< i don't need to go any further lol

(altho, this is all based on how these captains are seen fighting, if the creators wanted to, they'd prolly make renji beat anyone of em...that's why we're the veiwers not the writers =P)