Crowning Hashem with an inner will to serve

אמרו לפני מלכיות שתמליכוני עליכם.

"Recite before Me verses of Malchuyos (Kingship), so that you may crown Me as King over you."

On Rosh Hashanah, Hashem asks Bnei Yisrael to declare His sovereignty by reciting the Malchuyos verses, accepting ol malchus Shomayim (the yoke of Heaven's kingship) upon themselves.

דכ' ותרועת מלך בו.

As it is written: "And the trumpet-blast of the King is among them" (Bamidbar 23:21).

The shofar's blast expresses the longing of Bnei Yisrael to declare Hashem as their King.

כי באמת בני ישראל חפצים לקבל עול מלכות שמים עליהם.

For in truth Bnei Yisrael truly desire to accept the yoke of the kingship of Heaven upon themselves.

The inner ratzon (will) of every Jew is to be a servant of Hashem — that desire is real even when it is hidden.

ורחמנא לבא בעי.

And the Merciful One desires the heart.

What matters to Hashem is the inner heart's longing, not only the outward act.

ועבדי ה' אינם כעבדי מלך בו"ד אשר עושים כל תחבולות לצאת משעבוד המלכות.

And the servants of Hashem are not like the servants of a king of flesh and blood, who employ every scheme to escape the subjugation of the kingship.

A human king's subjects resent his rule and try to wriggle free of it; Bnei Yisrael are the opposite.

אבל בנ"י עושין כל תחבולות לקבל עליהם שיעבוד מלכות שמים רק שסט"א וכת דילי' מעכבין אותם.

But Bnei Yisrael employ every scheme to take upon themselves the subjugation of the kingship of Heaven — only that the sitra achra (the "other side," the forces of impurity) and its company hold them back.

The Jew's deepest effort is to draw closer under Hashem's rule; whatever resistance there is comes from the yetzer hara, not from his true self.

ולכן לא הביט און ביעקב כו' מאחר שבאמת רצונם להיות משועבדים אליו.

Therefore, "He has not beheld iniquity in Yaakov" (Bamidbar 23:21) — since in truth their will is to be subjugated to Him.

Because Bnei Yisrael's underlying ratzon is to serve Hashem, He does not regard their sins as their essence.

לכן מתמלא עליהם רחמים כמ"ש חז"ל מי שיש לו בן יגע בתורה מתמלא עליו רחמים.

Therefore He is filled with mercy upon them, as Chazal said: one who has a son who toils in Torah is filled with mercy upon him.

A father is moved to compassion seeing his child struggle to learn; so too Hashem is filled with rachamim when He sees a Jew laboring to serve Him.

שמייגע עצמו בתורה לידע איך לעבוד את ה':

For he wearies himself in Torah in order to know how to serve Hashem.

The very toil itself — striving to know how to do the avodah — is what awakens Hashem's mercy.

Summary: On Rosh Hashanah, Bnei Yisrael crown Hashem as King not as reluctant subjects but out of a deep inner ratzon to accept ol malchus Shomayim. Even when sin or the sitra achra holds them back, their true desire to serve Him remains — and that struggling toil to know how to serve Hashem awakens His boundless rachamim.