There is a discussion amongst the Rishonim whether the rule that one should greet his friend by using God's name ("והתקינו שיהא שואל שלום חבירו בשם" - Berachos 54a) is an obligation or merely a heter.
Rav J.B. Soloveitchik (also known as "the Rav") discusses1 this in הררי קדם (part two, number 124 (page 262)). The possibility that this was a heter, combined with the fact that the Rambam does not record this rule as practical halacha, convinced R' Chaim (the Rav's grandfather) that this was a temporary ruling (הוראת שעה), and that it is now forbidden to write "ב"ה" in correspondence. The Rav respectfully disagrees, based on Rashi's opinion that there is no real prohibition against using Hashem's name to greet friends.
The Rav concludes that the "new custom" of writing "בס"ד" on the top of letters is a baseless and meaningless custom ("ואין טעם ומקור למנהג זה"), based on a comparison to the laws of oaths -- an oath made in the name of Heaven, without invoking a name or reference to God, is not an oath. The purpose of this greeting is to use God's name, so referring to "שמיא" (lit. "Heaven") does not count.
1 The word "discussed" is used here in a loose sense. הררי קדם was written by Rav Michel Zalman Shurkin, based on students' notes from the Rav's lectures.