I suspect that the dichotomy isn't so much 'STEM vs Arts' but 'Accountable vs Unaccountable'. Most STEM fields are accountable to reality and future employers, and law is similarly accountable to rival scholars of law and employers of new lawyers. That makes law a rather noteworthy outlier in the liberal arts.
*in western countries
Do you know the M in STEM stands for 'Mathematics'?
Those fields are in neighborhood of STEM more than old "liberal arts" standard of language, foreign language, art (painting or music) and history. (Note: no ethics or philosophy.)
I’m skeptical that attainment of political power is easily attributed to a good liberal arts education. I think desire for power, some intelligence, and a relaxed relationship with principles go a long way. Well-crafted rhetoric...eh.
Who runs the world? Not STEM people. Most politicians have a legal and/or liberal background. They may also have a background in STEM - particularly likely in Europe, less so in the US - but you get nowhere in politics without studying and understanding foundational liberal arts skills such as rhetoric, persuasion, and public debate.
The idea that liberal arts majors spend their entire time writing on essentially useless activities - like post-structural critiques of famous literature - is hilariously naive.
Some liberal arts academics do indeed do this, but that's because the liberal arts have pure and applied elements. Just like STEM. And STEM academics also spend their time on wildly impractical theoretical pastimes.
But at the applied end, the liberal arts run the planet. They don't keep the lights on - engineers do that - but they set the policy goals and define the political, economic, moral, and philosophical orthodoxies that virtually everyone conforms to, whether or not they're consciously aware of it.