There's really no proof that an Awakening has anything to do with getting a keyblade. It's just a common assumption.
Sora's in KH1 didn't even have a keyblade in it, and he wasn't able to use the keyblade until the night of the storm.
Rather, the Dive to the Heart may simply have to do with the strength of your heart and the connection it has with others.
- In KH1, the dream may be indicative that Sora's heart has become strong enough to wield a keyblade. However, it's not like the Dive grants him the ability.
- In KH2, Roxas' Dive revolved around reconnecting with Sora, which just so happened to also give him the ability to use the real keyblade as opposed to the digitized version.
- We see the Dive again with Sora vs. Roxas, showing an inner conflict.
- Even in CoM, Riku has a Dive in which we witness him fight his inner demons with the help of Mickey.
- Ven's Dive in the beginning of BbS shows his heart connecting to Sora. Like with Roxas, this has more to do with the connection and less to do with the keyblade. Granting him the ability to use the keyblade again is an effect of the Dive, but not the purpose.
- Ven vs. Vanitas can be equated to a mix between Riku's fight in CoM (fighting his inner demons) and Sora vs. Roxas (coming to terms with oneself).
So, overall, while the examples we've seen so far deal with similar themes, there's no one reason as to why someone dives into their heart. It doesn't seem to serve a specific purpose, but basically acts as a metaphor for inner struggle/strength, or some other feat of the heart.