Let's say someone becomes bar mitzvah and decides to wear a tallit everyday, even though this isn't his minhag, because he wants the opportunity to make another brachah. Is this the right thing to do? And if not, should he stop wearing it?
See this article. It depends on how the custom originated, as that would dictate some of the rules.
I'm inferring from your question that the bar mitzvah boy inherited the custom from his father who did not wear a tallit until his marriage. The article says:
Rav Moshe Feinstein (Iggeros Moshe, Even Ha-Ezer 1:59) writes that there is no such thing as a local custom in America. Everyone who moves to America must keep their prior customs. Similarly, Rav Shlomo Zalman Auerbach (quoted in R. Yerachmiel Fried, Yom Tov Sheini Ke-Hilkhaso 19:5) rules similarly that Jerusalem has no single custom and no one who moves there may change his customs, except for a few unique customs accepted by all the communities there. However, according to the Pri To’ar, there is also a concept of a family custom. Even if you move to a place with an established custom, you still have to follow your family customs. Rav Yosef Shalom Elyashiv rules this way.2 Rav Hershel Schachter (“Hashbei’a Hishbi’a” in Beis Yitzchak 39, 2007) explains that some customs are family-based and some locale-based, although they are not always easy to differentiate. You must follow a family custom even if you move to a place that has a different custom. He adds that if you change families, you change family customs. One example is a woman who marries and, generally speaking, adopts the customs of her husband’s family. However, sometimes a man with little knowledge of his lineage (e.g. a ba’al teshuvah) marries a woman of prominent lineage and adopts her family’s customs.
Later, in the article, it says that one who wants to change customs must perform hatarat nedarim - annulment of vows.
From what I can tell, common practice is to follow Rav Schachter's ruling and stay with the family custom even when one moves to a different place.