Really love this thought experiment, and I can totally picture the Venn diagram. I suppose most of us who are fortunate enough to live in wealthy nations have achieved some measure of all 3 components, while 100% achievement of any is fairly rare. (If you consider "financial security" as part of the same continuum leading up to "financial independence." Perhaps 'intentional living' is the one you might argue is commonly lacking in a large portion of otherwise fortunate people).
But I gather what you're proposing is to take each of these combos to their extremes by imagining a life in which 2 of the components are completely met, while the third is completely missing. With that in mind, I'd like to take a stab...
1.) Financial Independence and Personal Freedom, without any Intentional Living - Trust fund baby is right! This person has all the tools, but has no idea what to do with them. He or she lets peers or pop culture dictate what to do with his or her time, what to purchase, what exotic locales to visit and take pictures of to then post on their social media accounts, and basically what to value. This is probably someone who many envy, but who very few are close to. I'm reminded of the Avett Brothers song 'Open Ended Life'
https://www.youtube.com/watch?v=b3YqxTjS2d82.) Financial Independence and Intentional Living, without Personal Freedom - This is a sad story, because it sounds like the person has worked really hard and made good choices, but lacks freedom due to something outside of his or her control. Perhaps a severe disability or illness. Or maybe they are responsible for a loved one who requires a lot of care. Or it could be someone who does the right thing 99% of the time, but who made one major poor choice along the way, like marrying the wrong person and feeling compelled to stay in the marriage no matter what (I know someone like this), or perhaps someone who committed a foolish crime and is now incarcerated. Regardless how you slice it, all of these pictures are grim, suggesting Personal Freedom is the most valuable of the 3, and the most difficult to restore when it is lacking.
3.) Personal Freedom and Intentional Living, without Financial Independence - At first glance, this seems to describe most of us, and isn't too bad a place to be in, especially if one is at least working toward the eventual goal of Financial Independence. However, reminding ourselves to picture a scenario in which this component is COMPLETELY lacking, it's much different really. Maybe this person was born in a very poor country, but still manages to kick ass at life against all odds. Or perhaps the person has taken a vow of poverty, whether literally or effectively, and given absolutely everything of themselves. Mother Teresa and Paul Farmer come to mind. Or perhaps someone much less over-the-top in generosity, but simply introspective, like a Buddhist monk, or anyone who finds fulfillment in basic subsistence without any guarantee of security whatsoever. I think this is someone I would admire, but it's not the life I would choose.
There's just no end to the number of directions someone could take this. I'd love to hear other people's interpretations...