The comparison you make isn't the best. Tsunade was introduced that way, same as Jiraiya who was mentioned to have a destiny of finding the child of prophecy. All of that story of Tsunade was provided to explain medical ninjas and her role as a Saanin.
About Sakura,
1) The story is about Naruto. 95% of the plot revolves around him. The best way to include Sakura as part of the plot is having her be Naruto's strongest supporter.
2) Sakura's entire story is not only supporting Naruto. Her medical skills have been brought up a fair few times,
a) Preparing an antidote and curing Kankuro when even Lady Chiyo couldn't.
b) Taking charge of the hospital and curing all the injured people during Pain's invasion.
c) Managing to fool even Kiba and poisoning them( remember Tsunade poisoning Jiraiya in part 1?).
d) Summoning Katsuyu and healing the entire Alliance in the Shinobi World War, Playing an important role in saving Shikamaru.
e) Even after all this chakra draining, still managing to save Naruto when all hope seemed to be lost. (Remember Tsunade and Shizune had completely run out of chakra at that point).
f) Possessing so much chakra that she, all by herself, helped Obito to use Kamui two-three times.
3) She is still young. She has already surpassed Tsunade in terms of strength. After this war arc is done, there is a high probability that her medical skills might be touched upon in the story.
It's not a good comparison because Tsunade was introduced that way?? What you're saying don't make sense at all. What does how the character was introduced have anything to do with anything? The way Tsunade was introduced doesn't change the fact that she had a goal and accomplished it.
1.) Sasuke's life isn't revolved around him. Gaara's isn't. Shikamaru's isn't. Tsunade isn't. That's a poor excuse when there are fewer characters (Hinata, Sakura) whose life revolves around him compared to who isn't.
2.) I'm talking about her goals and accomplishments, not what she does during her free time when she's not revolving around Naruto. Heck, even Hinata does something during her free time not stalking Naruto.
3.) Thats the problem. This is a 700+ chapter story and her goal will be brought up in the last 50 chapters? Sigh....