Unless one can find a way of somehow, even if not fully, inhabiting the mind of one's character. It can be done, though I'll be the first to admit that some are better at it than others and I'm by no means the best.
This, though, is the contention -- can you actually inhabit the mind of a character? You're asserting it's possible, and I'm saying it's not. What happens is that we get to a point where we may feel this way, but this isn't the same thing at all, and shouldn't be used to say that playacting with the goal of inhabiting the mind of your character as unattainable ideal is the best way to deal with social encounters.
Let's break this down a bit. Let's say I have a character that has a flaw where they will steal things. If I'm using your method, then I, as the player, must consciously choose to engage in this flaw, and will always be doing so with regard to the players around me. Any association of my character's desires to steal are only mirrored in myself if I actually share that desire -- there's no separation of the character and me at this point. This isn't inhabitation, though, because I don't actually change and become my character, but rather, my character is now just a reflection of me and how I think. When I choose to have my character steal, it's still a choice, and I'm probably weighing the choice against the risks in might engender in the game, whether or not I'll face social opprobrium from the other players for doing so, and so forth. The choice to engage this flaw is never one that originates or is based within the character, even if I'm rationalizing it as such. The engagement with the character here is performative.
And, that said, there's a huge amount of value and fun to be had doing this! Performative acts are part and parcel of a lot of entertainment activities humans like to do, not just RPGs. Do not read the above as any kind of dismissal or slight at this approach -- it's only meant to show that the belief that this is somehow a more pure or better way to engage with character is false, not that it's not a perfectly cromulent activity or approach! I quite enjoy performative aspects of play, so I'm not about to abandon this approach; I'm just not going to say that it's more pure than it is with regards to social activity or roleplaying in general.
Now, to contrast this approach, you can have a mechanical system that can engage the same thing. Here, a mechanical trigger would set off the character's flaw and thefts. There's quite a few ways to do this, so you can select for preference, but, to me, they all pretty much end up doing the same thing, whether metacurrency driven or check driven -- they force a new state onto the character. Here, as a player, your job isn't to choose for your character to engage their flaw (although you can usually still do this), but rather to accept that your character isn't you and has made this choice and then go with it. This puts the choice-making for the character sometimes out of your hands -- you aren't directing your character as a perfect representation of your wants and desires, but rather as an actual other person who does things that you might not. I've found that making the effort to realize that this is a different person I get to observe can actually improve my emotional connection to the character, meaning I'm feeling what this character is nominally feeling in that moment. This is also a very valid way to approach roleplaying a character, and can create surprising social encounters for everyone involved.
And, of course, you can mix the two -- choosing to engage character when you want and how you want with mechanical inputs coming in as well.
I'm the other way around, as through playing 3e I concluded that mechanics - toothy or not - tend to get in the way of roleplaying rather than aid it.
As others have said, the 3.x social skills are rather poorly put together, with hardcoded results baked in that do not at all reference the current fiction. There's a reason diplomancer as a term was invented. However, I always find it strange when people complain about skills that do this but are 100% perfectly fine with Charm Person and similar spells doing even more work. The usually deployed excuse of "it's magic" rings very hollow to me -- it's a circular justification that magic can such things because it's magic.
