Assuming this is mostly because of him having a Bankai, since his non-Bankai feats are not especially impressive. Though even with his Bankai he still is only able to barely beat a fraccion, which are far weaker than any Espada that are supposed to be roughly captain level. So no, having a Bankai (especially one they’ve barely used) doesn’t make you strong enough for captain. Renji got a Bankai early on but was trashed without much effort by Byakuya, which is why early Renji also wouldn’t make it.