One of the eight points that the gemara draws from the braisa is that המברך צריך שיטעום, when one uses a kos shel bracha, they need to actually drink from the kos shel bracha. I gave a shiur recently on the minhag in many shuls to say birchas hamazon on a kos after shalosh seudos, daven ma'ariv and then return to use the same cup for birchas hamazon. According to the simple reading of the gemara 102b and the Shulchan Aruch 299:4, this should be a violation of אין עושין מצות חבילות חבילות. See HERE for a halachic justification regarding that issue.
Another issue with the predominant custom is how one fulfills the requirement of המברך צריך שיטעום on the kos of birchas hamazon. This would be an issue even if one were to use separate cups for Birchas Hamazon and Havdala, since the drinking is typically not done until after ma'ariv. The Biur Halacha (299:4 d.h. mevareich) explains that as long as one generally makes birchas hamazon on a kos, they are able to drink from the kos of birchas hamazon even before havdala. The M.B. cites the Chayei Adam who holds that even if one typically doesn't use a kos for birchas hamazon, they can still drink immediately following bentching, before making havdala, so long as it isn't definitely night - ספק חשכה. However, in most situations people are not makpid to use a kos for birchas hamazon, and shalosh seudos ends at צאת הכוכבים, so drinking from the kos of birchas hamazon at that point would be a problem. The Biur Halacha writes that in a case where one cannot drink (either because he only has one kos, or because he can't drink before havdala), the Bach holds that one should make havdala on a kos of wine immediately, prior to davening ma'ariv, then drink from both the cup of havdala and the cup of birchas hamazon. Pausing to daven ma'ariv would be too long of a break between the birchas hamazon and the drinking from the cup. This is also clearly the opinion of the shulchan aruch ha'rav. But, the Biur Halacha quotes the Derech HaChayim who says that it is fine to daven ma'ariv in between, which is the minhag ha'olam.
It seems to me that the reservation of the Biur Halacha is correct, and davening ma'ariv between the birchas hamazon and havdala is a problem because the drinking after havdala would not be effective for the kos of birchas hamazon, and would undermine the entire advantage of being bentching on a kos. The Rashbam explains that from the fact that we don't tell the person who needs to eat on Motzei Shabbos and make Havdala, to first make havdala, then eat, then bentch and drink the kos, implies המברך צריך שיטעום. But why is this a violation of המברך צריך שיטעום, he will drink from this very kos after bentching and that would qualify as the the drinking for both the havdala and the birchas hamazon? Clearly, the Rashbam holds that eating a meal between havdala and birchas hamazon would be too much of a hefsek and not allow the drinking to go back on the havdala. Just as the meal would constitute a hefsek, and therefore not allow the drinking afterward to qualify as המברך צריך שיטעום, so too the davening would constitute a hefsek as the shulchan aruch ha'graz holds, not like the minhag ha'olam and not like the derech hachaim.