I would argue that judicial review developed in the United States because it was very much consistent with the core ideas of the Constitution, even if it was never specifically mentioned in that document. Judicial review is consistent with two of the main ideas of the Constitution: checks and balances/separation of power and limited government.
One of the major ideas in the Constitution is that the government cannot simply do whatever it wants. The government, like individual people, must be subject to the rule of law. If it is not, the government will be able to infringe on the rights of the people and the people will have no true freedom. Judicial review is a good way to ensure limited government since it can prevent the elected branches from doing things that are unconstitutional.
The Constitution tries to ensure that government will remain limited by separating the powers between the branches of government and allowing them to check one another. It would not make sense to say that Congress has the power to determine for itself whether the laws it is making are constitutional or not. It makes much more sense to have that power be vested in the judicial branch so that the separation of powers will be more complete and so the judiciary can check the elected branches.
I would say, then, that judicial review is so consistent with the Constitution that it developed naturally even though the Framers did not explicitly give that power to the judicial branch in the Constitution.