High-quality (higher carbon) steel required for frame, chain and gears was not abundant enough and cheap enough until late XIX century.

You know if you tap on the text at the top, it takes you to an article that expands upon the question. In this case you'll find that article discusses the strengths and weaknesses of the materials bottleneck!

Agreed, and also chain and fasteners specifically require the ability to mass produce very small, very strong, very consistent parts. This necessarily needs production lines with consistent tooling and quality assurance.