No flips for you!
I think this really gets to an important point -- when we're freeform roleplaying a social situation, it's very easy to elide or gloss over difficulties in the situation, especially if we're keenly aware that pressing those things and complicating the situation can lead to opprobrium from other players ("man, why'd you bring that up?"). A system where things are clearly established and have to be addressed can be very preferable if the goal is to actually inhabit the situation the PCs find themselves in. Way too often I've had a freefrom RP encounter end up not addressing a point because the play just moved past it with how we were "yes, and"ing each other. Sure, a dedicated GM can probably handle this, but this is putting the entire load on the GM to manage and push the situation, rather than the responsibility of all of the players, and actually engenders the "get the teacher on a tangent" approach where distraction from a problem is solid play rather than addressing it.While I view having more well rounded characters who can participate in more types of scenes as a good thing what I like even more are having niches within a given type of encounter so we can have more diverse and interesting sorts of social encounters and sorts of exploration encounters where players have to work together to be effective just like they have to in combat.
Even more important to me when it comes to social scenes (which most of the games I run tend to heavily skew to) is keeping the focus on the fiction. A well designed fiction first social influence system like we get in Hillfolk, Dogs in the Vineyard, Chronicles of Darkness, and Exalted Third Edition amongst others keeps the focus on the fiction and prevents us from ignoring salient bits of the fiction in order to get the result we want. Often I find that when we just play out conversations at the table it can be easy to filter out important details when they are inconvenient. A good social influence system can help keep the focus on the fiction and prevent us from getting too caught up in our conceptions of who these characters are. It can also really help situations that should be tense not fall prey to our natural agreeableness.
That last bit can be a big problem for me. Not so much for some other people I bet.
There's also the issue that, quite often, social encounters are confrontational and/or heated between PCs and NPCs. This is hard to do and maintain the atmosphere of a friendly gaming table. If I allow myself to connect to the character, then I should be feeling angry/frustrated/scared/etc and this makes it very hard to not have it bleed into the play at the table. Freeform RP has very little in the way of firebreaks or safeguards here outside the social contract to not go too far. This is another area where system can step in and provide a structure so that I can connect with my character but it's not directed at the table at another player -- it more contained within the boundaries of the system because it's the system that's mediating the resolution, not Bob.
You can get into all of these things with freeform RP, and it can work out wonderfully, but it's going to be very uncommon and require a very good set of table understanding and social contract rules to enable it, alongside some rather special players/GM. When done this way, I'm sure the payoff is great. But, I'm not in that situation, despite playing with friends and people I like and respect, and having tons of experience. I find that I get closer to this when I'm using a system that enables it, and provides the feedback/firebreaks as necessary to keep it all in the game and off the table. I've never once become frustrated with another player during a Blades game because I'm not competing with them for resolutions by playacting and being stymied by an immovable position -- instead, we all try our thing and find out what happens next through the mechanics.
Now, I still love my freeform RP, but I don't play games where I'm really trying to connect to a character or drive hard on character traits when I'm doing so -- I'm having a good time with friends playing pretend elves.