Few of us do public policy on a daily basis, but many of us have opinions on it, and of those that don't most of us have friends that do. Not that having correct policy judgment buys you much in that context, consequentially speaking; I think the hedonic implications would probably end up being decided by how much you need to keep beliefs on large-scale policy coherent with beliefs on small-scale matters that you can actually affect nontrivially.

Wouldn't a rational consequentialist estimate the odds that the policy will have unpredictable and harmful consequences, and take this into consideration?

Regardless of how well it works, consequentialism essentially underlies public policy analysis and I'm not sure how one would do it otherwise. (I'm talking about economists calculating deadweight loss triangles and so on, not politicians arguing that "X is wrong!!!")

I think the central trick is that you don't aim at the ultimate good in public policy, just things like fairness, aggreegated life years and so on. You can decide that spending a certain amount of money will save X lives in road safety, or Y lives in medicine, and so on, without worrying that you might be saving the life of the next Hitler.