If he is a friend and he wants to play with you, then you would party as FFA or instanced loot and can alternate the choice upon each game creation. Using the same characters, you could have your first game session as FFA. Then the party leader creates a new game where the personal loot option is selected.
The other issue your hypothetical exposes is that you and your friend have different preferences. In this hypothetical case, you prefer FFA and he instanced loot. Your “FFA-only” makes you happy because that is what you prefer but eliminates your friend’s choice and what your friend prefers. I find common ground with my friends and respect their preference when I disagree. I do not eliminate their ability to choose what my friends prefer to do. (Of course, I mean here, that their preference is not illegal or highly morally objectionable, etc…)
The next curiosity of your hypothetical relates to the frequency of D2R players who prefer FFA or personal loot if both were selectable options.
If players prefer FFA >>> personal loot, it is far less likely that your friend would prefer instanced loot. As such, having both options exists would be highly unlikely to cause this hypothetical situation to occur in the first place.
If player preferences were more evenly this split, your hypothetical is more likely. However, this shows that the population is divergent in their views.
If player preferences were personal loot >>> FFA, then by not having personal loot as an option, FFA-only would disenfranschise the vast majority of the playerbase.