@Alex kindly directed me to this audio shiur by R Aryeh Lebowitz who discusses this question. In summary, he says that
- there have been a number of nuschaot (texts) proposed for a shorter birkat hamazon, originally for cases of urgency (shaat ha'dchak)
- recently, poskim such as R Yitzchak Abadi have suggested using them in all cases (lchathila), since people have a hard time concentrating for the whole length of birkat hamazon, arguing it is better to have more concentration for a shorter text
- he reminds us the gemara (Brakhot 48b) writes the blessings of Birkat Hamazon were composed by no other than Moshe, Yehoshua and David and Solomon
- the Tur, Beit Yosef and Shulhan Aruch give specific requirements for the minimum to be included; the Magen Avraham quotes an abbreviated text for birkat hamazon for urgent cases that satisfies all these requirements
Additional reasons why R Abadi suggested his text is that
- some people were using shortcuts and not saying birkat hamazon for certain foods (e.g., on pizza, or pita/falafel), chosing instead to say incorrectly borei minei mezonot and the relevant bracha ahrona
- everything one needs to say is in the shorter nusach so there is nothing to lose by saying it
R Lebozitz personally comes out against using such shortened texts. Interestingly, R Abadi himself doesn't use his own shorter nusach !