During my Yeshiva days this question was posed several times during Elul...
1. R"H is the day of Judgment
2. Y"K is the day of atonement
3. Why not get forgiven BEFORE getting judged? IOW Y"K should precede R"H, and we'd be judged with a Clean Slate.
The answer I usually heard was:
A1. It takes the serious nature of the Yom Haddin on R"H in order for us to take Y"K seriously
Without disputing that rationale I have a different approach
A2 Namely, that this issue was actually the impetus for Y"K style S'lichot which precede R"H.
EG The Rambam mentions saying S'lichot AFTER R"H before Y"K. Subsequently, someone may have reasoned that model as inadequate and pushed S'lichot to an earlier date.
This also helps to explain the long Erev R"H S'lichot as a common minhag to fast at least part of the day on Erev R"H, in order to provide a form of Y"K Katan before the Yom Haddin
Best Wishes for 5773!