For one, how is it any different when Jews say a bracha over anything else? Jews say brachot over food, smelling fragrances, lighting Shabbat candles, when we hear thunder, and many other instances. It does not mean we are worshiping the items, but sanctifying them in a moment of holiness. This would explain why one only glances at the moon briefly before saying the bracha rather than staring at it the entire time and fixating upon it. The prefatory Psalm 148 reaffirms this notion.
We become closer to G-d by appreciating His creations, which is why anyone who blesses the new moon is as if he has greeted the Divine Presence (Babylonian Talmud, Sanhedrin 42a). After blessing the new moon, one uses the moon's light to recognize one's friends and co-religionists and to wish them Shalom Aleichem. Shalom Aleichem reminds us that because humans are created in His Image, we also greet our fellow man and wish him well.
Symbolism of the moon also plays a pivotal role in bringing meaning to the practice. The monthly reappearance of the moon engenders a sense of renewal. Renewal helps us gain a sense of strength and hope, which is supposed to bring us joy. There is also symbolism in the moonlight. Much like the moon waxes and wanes, we also have high points and low points in life. Moonlight illuminates in darkness. We can make it through in dark times because of the moonlight, which is why we should be appreciative of the moon. Unlike other brachot, which do not highly recommend the use of a minyan, קדוש לבנה does. The fact that it is optimal to recite the bracha with a quorum of ten shows us that we don't have to face the darkness of life alone.
Additionally, R. Menahem HaMeiri points out that wonders of nature are a reflection of G-d's presence, which requires us to praise His greatness. During קדוש לבנה, we recognize G-d's might and control over nature (Beiur Halacha 426:2). We further recognize His strength by reciting Aleinu afterwards.
קדוש לבנה is much more than just howling at the moon. קדוש לבנה provides us with a monthly encounter with the Divine that helps us get closer to G-d and appreciate His creations.