Given Birkat Hamazon’s importance among blessings, the Gemara (Pesahim 105a) discusses whether warrants being recited over a cup of wine. To clarify, this refers to the practice of filling up a cup of wine before reciting Birkat Hamazon and then reciting “Bore Peri Hagefen” once Birkat Hamazonis completed. The Shulhan Aruch (Orah Haim 182:1) lists three opinions based on the Gemara’s discussion: i) Birkat Hamazon must always be recited over a cup of wine, even by an in individual, ii) a cup of wine is only used when there are three or more participants in the Zimun and iii) a cup of wine is never required for Birkat Hamazon. It appears that the Shulhan Aruch leans towards the third approach, although the Rama (ibid.) writes that the optimal way to fulfill the Mitzvah of Birkat Hamazon is over wine.
The Aruch HaShulchan (Orah Haim 182:1) explains that the widespread practice of not reciting Birkat Hamazon over wine is due to the high cost of wine, especially in those days. As such, one could reason that since wine is relatively affordable, one should recite Birkat Hamazon over wine. Nevertheless, Rabbi Moshe Feinstein (Igrot Moshe, vol. 2, Yore Deah, § 52:3) writes that since nowadays people are accustomed to not using a cup of wine, one need not be strict in this regard, even in a Birkat Hamazon that involves many participants. Siddur Avotenu as well as numerous Moroccan rabbis write that the custom was to only use a cup of wine during Sheva Berachot, but not in other instances. Furthermore, Rabbi Shalom Messas (Shemesh Umagen, vol. 2, Yore Deah § 29) says that even at Sheva Berachot it was not common for Birkat Hamazon to be recited over wine, and this appears to be the custom.
The Kaf HaHaim (O.H. 182:1) writes that based on Kabbalah, one should be strict and recite Birkat Hamazon. Although a worthy stringency, this is not a requirement. Indeed if one does use a cup of wine, one should say that one is doing so “Bli Neder”, lest such a practice take on the status of an oath and one be Halachically obligated to continuing doing so.
Summary: The Moroccan custom is that Birkat Hamazon is not recited over a cup of wine.