Mr. Mander wrote:
In series like Bleach and DBZ, they become more powerful as soon as they decide they need to be.
Not really. In Dragon Ball, they become stronger because they train hard and long to become stronger, not by snapping their fingers. In Dragon Ball Z, the Saiyans become stronger by almost dying (and it doesn't magically heal them, looking at you Kubo) and through anger, because it's one of their races' properties. Contrary to Bleach, the Super Saiyan form isn't pulled off the author's booty since they talk about it earlier.
Even then, acceding to another state of Super Saiyan is not just "lol I wanna be strong" or "I'm gonna fight myself in my head", to become SS2 you need to voluntarily let anger control you and it requires a shitload of willpower (or training, since Goku & co can later pull it off without getting too overwhelmed by their anger). SS3 is also reached by more training since it consumes insane amounts of energy. Piccolo becomes stronger by syncing and fusionning with people of his race. Freezer doesn't become stronger, he simply removes the limits he imposed on himself in order to not destroy the worlds he's trying to conquer. Cell becomes stronger by assimilating people, and so does Boo (even though, arguably, assimilating people only gives him more techniques). Little Boo is the strongest of all Boos because Vegeta removed the only "good" part of him, letting his raw power run free.
In Bleach you gain power because you have it already but your soul, that is also your sword, basically says "nope, not gonna let you access your power because I want you to fight me in your imagination" while your friends are dying and stuff.