“A simple causal chain makes historical transitions look automatic”

Yes, you understood the problem correctly.

A causal chain is a sequence in which one event or condition contributes to another.

Your chain is approximately:

legal freedom → free labour → capitalist employment → working class → some upward mobility → some middle-class formation.

The problem with a simple causal chain is not that having a chain is inherently wrong.

The problem arises when the chain is presented as though each step automatically produces the next.

Example of an overly simple chain

Emancipation → factory employment → wealth → middle class.

That wording makes it sound as though:

1. emancipation automatically produced factory employment;
2. factory employment automatically produced wealth;
3. wealth automatically produced middle-class status.

But historically, many things could intervene.

For example:

Emancipation → legal freedom → search for employment → availability of industrial employment → actual employment → wages → savings/skills/business experience → opportunity for advancement → successful advancement → middle-class position.

Not every person necessarily passed through every stage.

Your argument is different

You are not claiming:

A automatically produces B.

You are claiming:

A created the legal condition that made B possible, and B subsequently created opportunities for C.

That is a much more precise causal argument.