TVTropes calls adding non-pronounceable characters to a works title a "Lucky Charms Title" and as you can see from the example list, it is not a purely Japanese phenomenon. However, the Japanese are generally more adventurous with this. An explanation could be that because of the huge amount of Kanji the Japanese written language contains, being suddenly confronted with a character you can not immediately identify is not as jarring for a Japanese reader as it is for a Western reader.
Why is the Unicode character WHITE STAR (☆) so popular? Because it is a natural eye-catcher. When looking at a list of works, like a TV program for example, the ☆ character immediately stands out, even among the huge number of characters the Japanese language is using.
By the way: Official releases in English often drop the lucky charms from the title. Amazon sells Lucky☆Star and Puni Puni☆Poemy sans ☆'s (although the star usually still appears as a decorative element in the lettering on the cover to reproduce the original typography as faithfully as possible).