HH Shulchan Aruch, Even Ezer 136, Bair Haitiv brings not to divorce on Erev Shabbos. Reasons given, a. It's a busy day and mistakes can be made. B. Some ruling of courts are not done on Erev Shabbos. All agree that it is just an optimal extra precaution, not binding. IMHO probably more to do with the first divorce on Erev Shabbos....
Na NaCh NaChMa NaChMaN MAyUMaN