His ambition reflects his origins, he was just a normal guy who was literally pulled into another world trying to save someone. Very much like Urameshi without the veneer, he becomes a Shinigami in order to protect. From there it simply expands from his friends and family to literally everyone & everything he can, entire worlds. Ichigo never stopped being a normal guy dealing with increasingly weirder shyt but all ge ever seeks out is normalcy because he was robbed of that as a child.
Kubo obviously felt the same which is why instead of becoming a Squad Captain or Royal Guard, he ends up a 27 year old writer with a PhD. All the rest want extraordinary things because that's what they were born into (Luffy, Naruto, Shinra, Deku, etc.) but that's not nor has it ever been Ichigo's bag.
It's a journey for most characters, getting the title is the end. Ichigo wanted power to protect, almost immediately gets it, and spends the series learning how to deal with it without allowing it to consume him thereby risking what he actually wanted to protect: regular boring life.