I think that trolley problems contain perfect information about outcomes in advance of them happening, ...

True.

... ignore secondary effects, ...

Depends on what you mean. The problem is stated with a simple question: do you push the lever / fat man? You are not instructed to ignore whatever effects it may have. A trolley problem may be stated with some additional remark like "nobody will ever learn about your choice" which can implicitly suggest to ignore some possible real-world effects, but that isn't inherently present in every trolley problem.

... ignore human nature, ...

No. Some answers to the dilemma tend to ignore human nature, but the problem itself doesn't. And of course, there are many moral questions whose answer is both natural and correct with respect to whatever ethical theory we use, but those wouldn't make a good material for interesting and non-trivial discussions about morality.

... and give artificially false constraints.

True.

Now, I think that's bad. Agree/disagree there?

Disagree. You object to the fact that the trolley problem is an idealised scenario. I see that objection about as equally valid as an argument that formal logic is bad because it ignores biases and heuristics that all real people use.

... I think this kind of thinking seeps over into politics,

Any kind of thinking about decisions and morality can seep into politics. I don't think that too much reductionism is a frequent problem in politics, but even if it is, it is a problem of any formalised decision theory, or social science in general.