The Wrights did extensive experimentation, on both models an full-sized prototypes. They built the first wind tunnel and developed calculations for lift and propeller thrust.

They also practiced fairly rapid design iteration, trying out ideas and adapting to actual experience. What they arrived at worked, though it was far from ideal and doesn't much resemble modern aircraft (beyond the notion of wings and the rough principles of control surfaces). Once other designers / engineers entered the field, and with more reliable engines, further iteration advanced rapidly.

Military aircraft played a significant role in WWI, only a decade after the Wright's first powered flight.

> He identified the four forces which act on a heavier-than-air flying vehicle: weight, lift, drag and thrust. [...] He also designed the first glider reliably reported to carry a human aloft. He correctly predicted that sustained flight would not occur until a lightweight engine was developed to provide adequate thrust and lift. The Wright brothers acknowledged his importance to the development of aviation.

— https://en.wikipedia.org/wiki/George_Cayley

I think by the time the Wright brothers came around, the general theory for powered flight was in place. The Wright Flyer was precision engineered, compared to most 'kites' that came before it. It's not every day you see an internal combustion engine on a kite.

And what, there's nobody between Archimedes and the Wright Brothers I could have been referring to? Whatever...