On a simple level, Ibn Ezra tells us that this lowly dress would shame the monarchy.
According to the Me’am Loez, people were not allowed to wear sackcloth before the king because it was considered a bad omen as such people would thereby be walking reminders of death. For this reason, we find in the Torah (Bireishis 50:4) that when Yaakov passed away, Yosef was not allowed to have an audience with Pharoah.
Also, the Talmud (Brachos 62b) learns a kol v’chomer (a fortiori) argument that if in our verse, a person could not wear sackcloth (which, although is ugly, it is not repulsive) before a human king, how much more-so should one be forbidden from spitting (which is physically repulsive) in a synagogue, where one stands before the King of kings.
The Kabbalas Rabbah takes this idea one step further. If it is inappropriate to walk in front of a hum king looking like a mourner, how much more-so is it inappropriate to appear before the King of kings looking that way. In other words, in general, having a downcast negative attitude does not befit the servant of H-Shem. Even on the night of Rosh HaShanah, when we are judged, we are instructed to leave the synagogue confident in our positive judgment.