I think it's more productive to view the political tableau through the lense of centralisation/decentralisation.
Discussion
Also interesting piece of history, the term left-wing and right-wing dates back to the days after the French Revolution , when the old order and the new order had to resume parliament, and such was the hatred between them that they stood on opposite ends of the room.
Both socialism and (fiat)capitalism when viewed through the lense of left vs right seem like they diametrically opposed to each other, but when viewed through the lense of centralisation vs de-centralisation, we see infact that the end result is one and the same : more and more power and influence in the hands of fewer and fewer people.
I prefaced the word capitalism above with (fiat) because we do not truly have free market capitalism under a fiat standard.
The founders warned us against central banking, and fractional reserve banking. We did not listen.
Theres a theory that Lincoln was killed because he rejected fractional reserve banking , insteading prefering his gold redeemable "Green Back Dollar".
Theres yet another theory that this was actually what "The Wizard of Oz" was really about.