The sense I've gotten so far is that given a causal model with non-controversial causal assumptions, you can do algebra in some cases to come up with conclusions that otherwise (in the absence of do-calculus) would have required experimentation. And in other cases, you're still stuck.

What kind of answer do you expect?

You can get no causality from data alone. You always need additional assumptions.

If you can do an intervention and manipulate a variable as you wish, the assumption of its independence is warranted. A correlation with the outcome indicates a causal path (or you're being [un]lucky). Even in that case a more complex causal model is useful to get better estimates, distinguish direct and mediated effects, etc.

If you have observational data only there is not much that can be done without a causal model. Given a model, the causal effect of one variable on another may be estimated in some cases. But if your model is wrong you may conclude that there is an effect when none exists or deny the existence of a real effect.

I think I expected the book to better live up to its billing. Here is an excerpt from the in-sleeve summary:

"Beginning with simple scenarios, like whether it was rain or a lawn sprinkler that got a sidewalk wet, the authors show how causal thinking solves some of today's hardest problems, including: whether a drug cured an illness; whether an employer has discriminated against some applicants; and whether we can blame a heat wave on global warming."

In all of these "hard problems", it is the model itself that is the most contentious piece, and the most ideological. Some people have a mental model where CO2 produced by humans is causing climate change (which I agree with), and others believe that the changes can be explained by natural fluctuation. These beliefs are undoubtedly influenced by a person's biases. It's not very useful to say "once you have accepted a causal model, you can draw lots of useful inferences." Because the main point of contention is over what is causing what.

I found this statement of yours honestly more useful than anything I read in the book so far: "You can get no causality from data alone. You always need additional assumptions." The downside of this is that different people can make different assumptions, and so this implies that this kind of causal analysis can't mediate disagreements between different groups of people who see the world very differently.

> It's not very useful to say "once you have accepted a causal model, you can draw lots of useful inferences." Because the main point of contention is over what is causing what.

Well, accepting a causal model and drawing lots of useful inferences seems better than drawing lots of misleading inferences because no attention is paid to the model (or being unable to make any inference because it's not obvious how the data can be used).

Even if people may not agree on what is the right model at least this approach makes the model explicit. And in many cases there is no reason for disagreement, but if there is no careful analysis the wrong model may be used by mistake. For example, chapter 8 has an extense discussion of the potential outcomes approach in the context of salary as a function of education and experience.