Instead of using closed form, they can easily computed with the approximation of the curve with segments, and you place the points where there is most curvature or where the 1st derivative isn't close to zero

Yes - but there are other curve classes (like P-H) that have an exact solution and don't need approximation. Bezier curves have tons of nice properties but also a lot of shortcomings, for example not being able represent conic sections like circles and ellipses without introducing weighting (rationals), which complicate computations even further. So, depending on what you're doing with them, it's worth exploring other curve types IMO.