Judicial Review: It's not that hard, is it?

I'm currently reading an excerpt from Alexander Bickel's book The Least Dangerous Branch, which is largely an attack on the idea of the power of judicial review, for my civil liberties/democratic legal theory class. The passage I'm reading and getting infuriated with at present is one in which Bickel asks why, even if we accept that a law contrary to the Constitution is invalid, the courts ought have the power to invalidate it. He goes through this long, long process of asking why this power might rest in the courts, which I'm not even to the end of yet, but it strikes me that it's really not very hard.

If Congress purports to pass a law X which is, in "truth," unconstitutional, then it is not actually a law. From time to time the occasion may arise for a court, possibly the Supreme Court, to decide a case or controversy where the issues that must be raised by the case in order to decide which side should triumph involve the question of whether that law is a valid law or not. In such a case, in order to do its basic, fundamental job, that Court must decide whether it thinks that law X is constitutional. If it decides that it is unconstitutional, then it must grant victory in the case to the party whose argument depends on the law's being invalid. Going forward, under the principles of stare decisis, potential plaintiffs have a reasonable expectation that, should another case arise involving the question of whether law X is valid, that court and all courts inferior to it will hold that law X is not valid. When we say that a law has been negated by judicial review, this is what we mean: that everyone in the country can expect that, should the question come before a court, that court will say that the law is invalid, and render its decision accordingly.

Note that this logic, which strikes me as extremely sound, does not argue against departmentalism, Thomas Jefferson's view that Congress, the courts, and the President can all interpret the Constitution independently, with no branch having the final say. The point here is that the courts will interpret the Constitution as they must to do their own job. What gives the judiciary the appearance of being the "final" arbiter of the Constitution is the simple fact that, if you stipulate that either Congress or the President has acted in a way contrary to the Constitution, it is extremely likely that someone somewhere will have a valid case or controversy they can bring before the courts. Once the question gets through the door of a courtroom, the parties to that particular case are bound by the judgment of the courts. Therefore, it is extremely rare that anyone can act in a way that someone cannot make the judiciary's business. In situations where it happens that there's no way to make a judicial case out of the matter (as, for instance, a potential decision by the Obama Administration that the debt ceiling was unconstitutional), quite defensibly we arrive at a departmentalist arrangement.

All of this doesn't even address the main questions of whether judicial review is undemocratic or not, which it is, Bickel's objections to the contrary. We're just talking about whether courts have it in our own system, and it strikes me that you need to go through some contortions to avoid the conclusion that they do, according to the logic I've sketched out above.