Mordecai refuses to bow because he knows what real power looks like.
In Targum Sheni on (Esther 3:3), the royal servants press him to kneel before Haman. Mordecai answers with a vision of the One before whom every created thing moves. He bows only to the living God in heaven, whose angels are fire, who holds the earth, spreads the heavens, darkens the sun, lights the darkness, and binds the sea within its borders.
The speech is cosmic because the pressure is political. Haman's greatness is an order of the court. God's greatness is the order of creation itself. Mordecai points to the sun, moon, stars, planets, sea, firmament, and angels as witnesses that no mortal official deserves worship.
His refusal is not stubbornness for its own sake. It is a hierarchy of reverence. A human king may command service. An officer may demand honor. Bowing belongs somewhere higher. Mordecai stands at the palace gate and answers empire with creation.
Never! I only bow before the one great and living God in heaven, who is a consuming fire and whose angels are fire, who holds the earth in His arm, who spread out the heavens by His mighty power, who by His will makes the sun to be darkness and the darkness to be light, who by His wisdom surrounded the ocean with sand, provided the sea with odorous salt and with banks, keeping the waves bound in the deep as with chains that they should not overflow the land and not pass their limit. By His word He created the firmament and spread it as a cloud in the air, yea. He spread it as a vapour upon the world, and a tent upon the surface of the earth, and by His power He carries the things that are above and below. Before Him the sun, the moon, and the Pleiades run their course, and the stars and planets are not for a moment inactive. None of them rest, but all run before Him as His messengers, who go right and left to do His will. To Him who created them belongs praise, and before Him one must bow."