I actually disagree with everything you just said. He doesn't just wanna protect his friends and family. Yes that is his characters writing explicitly but he enjoys fighting and kicking ass. He is petty and has a massive ego and it hurts when enemies stomp him. He wants to get back at his enemies, in fact in its most extreme case it gets in the way of protecting his friends( Ichigo telling Orihime to heal Ulquiorra so he could fight him himself). . This side of his character is almost always implicit which is why Kubo is such a talented writer. Remember how Ulquiorra stopped his Getsuga tenshou with his bare hands? He got back at Ulquiorra by stopping Ulquiorra's spear at point blank range in Vasto Lorde form. He did the same thing against Aizen. Remember how Ichigo stopped Aizen's sword wit his hand and what he told him? It's also why he didn't instantly kill Byakuya back in soul society arc. He wanted to get back at him for making fun of his small bankai and also for absolutely destroying him back in human world. If he just wanted to save Rukia he could have just killed Byakuya right there and then. Another instance I can think of right now is his fight against Grimmjow. I think he was actually enjoying that fight so much that he held himself back just to drag the fight. And when Orihime yelled his name he kind of came back to his senses. It reminded him of why he was there so he stops Grimmjows claw and says " sorry Grimmjow, I have to end this".