The answer to this question lies in the fact that "we always read Parshas Bamidbar before Shavuot" [Shulchan Aruch, Orach Chaim]. Before we experience the giving of the Torah once again - for spiritually the Torah is given anew every Shavuot - it is necessary to recall and take to heart the fact that the Torah was not given in a civilized environment, but in a desert.
The lesson here is twofold:
1. A desert is a place of utter desolation where "no man can live". Thus the Torah was given there to indicate that it should be embraced without any preconceptions or ulterior motives. When a person lives in a civilized place and he encounters a new idea or suggestions, he will first evaluate it to determine whether it is acceptable according to societal norms. With Torah, however, this would be a mistake; the correct approach to accepting the Torah is "we will do, and (later) we will understand" (Shemos 24:7). Therefore the Torah was given in a desert, where nobody lives, to indicate that one needs to be truly "open-minded" - i.e. not influenced by one's environment - to appreciate its values.
2. The Torah was given in a desert to teach that sharing the Torah with those who currently find themselves in a spiritual desert is fundamental to Torah Judaism. It is not the case that the Torah can "also" reach those who are found in a spiritual wasteland; to the contrary, this is a central theme of the giving of the Torah: To transform every spiritual desert into a "civilized environment".
Based on Sichas Shabbos Parshas Bamidbar of the Lubavitcher Rebbe (5732 and 5734)