Of course both De Castlejau and Bézier were building on other tools developed previously: Most importantly, Bernstein polynomials, which were developed by Bernstein in service of a constructive proof of the theorem that every continuous function can be approximated arbitrarily well by a polynomial. You can read about that history here https://doi.org/10.1016/j.cagd.2012.03.001https://www.researchgate.net/profile/James-Peters-3/post/Sin...
From memory, I recall reading that there was work done by a french mathematician that didn't seem to have much applicability until the advent of 3d modeling.
I'm probably wrong here, it's mostly from memory some 20 years ago. But having said that, I think the overarching point is still valid, it's often the case that someone does something to explore and an application for it is discovered, sometimes posthumously.
De Casteljau and Bézier were both French mathematicians paid by different French car companies to work on systems for doing computer-aided design for cars, because of advantages vs. building physical scale models.
Bernstein was a Jewish Ukrainian mathematician who studied in Germany and later worked in Moscow, and his main research was about partial differential equations, probability, and function approximation, three "applied" topics. (Of course all of these topics also have theoretical aspects; such is the nature of mathematics.)
Of course both De Castlejau and Bézier were building on other tools developed previously: Most importantly, Bernstein polynomials, which were developed by Bernstein in service of a constructive proof of the theorem that every continuous function can be approximated arbitrarily well by a polynomial. You can read about that history here https://doi.org/10.1016/j.cagd.2012.03.001 https://www.researchgate.net/profile/James-Peters-3/post/Sin...