Why isn’t yom kipur before rosh hashana Answer 2

To restate the question…On yom kipur we wipe away our sins. On Rosh HaShana we proclaim HaShem as King (no sin-mention). Surely Yom Kipur should go first so we can proclaim HaShem as King in a state of sin-free purity? (as inkeeping with the rule of ‘sur mera v’asei tov’)
An(other) answer is based on a lovely comparison. The Rambam (hil melachim 1;1) comments that we were commanded 3 mitzvos upon entry to the land of israel; 1st to appoint a king, then wipe out amalek, and finally to build a beis hamikdash. [and that is the order that they occurred in nach.] The order is very precise here. So too, Rosh HaShana is compared to appointing a king (we ‘appoint’ HaShem as King), Yom kippur to the removal of amalek (amalek is the embodiment of sin), and Sukkos to the beis hamikdash (a surrounding sanctuary of HaShem’s Presence).

Thus, for the same reason a King is needed to beat amalek, so too is Rosh HaShanah needed to have a successful yom kipur. (this borders on the first answer I suppose!)