Who would perform the function of determining whether legislation is constitutional?
Who determines it in the first instance (and often the final instance) now?Lower level federal and state courts have final say in most case volume.
Well good thing it is not democracy, for we already have two democratic branches, and we need at least one branch that is separated by at least one degree from the whims of the majority.
Now, in a strictly "positive" sense it is true that since the Court is not particularly democratic so therefore purely from the point of its own self-interest as an institution, must be careful when wielding its power in a way that has significant policy consequences, particularly when it comes to policies that are politically explosive. For this reason I doubt the Court would move toward something like abolishing the death penalty, particularly if crime rates are as high as they have been for the last 30 years and the death penalty remains popular. There are no death penalty abolitionists on the Court today, unlike 20 years ago, and there are at least 4 strong conservative votes young enough to outlast 8 years of Obama. The Court is still more inclined to shift Right than Left, but if it is smart it will stay 'conservative', at least where hot-button political issues are concerned.
As for constitutionalism, that is potentially different. Note that a radical constitutional decision, one that say... departs significantly from previous legal doctrine to reach into relatively new and untraveled areas, and which has significant implications for a large number of future cases, does not necessarily have to have significant policy implications. On the other hand, a decision which merely applies a long-held legal principle to a new case could have earth-shattering policy implications. Generally it is the latter that will receive attention outside of academia, not the former, even though the former is "constitutionally" more radical.
And also it is true that our legal system is a social institution and like all social institutions it has evolved over time. And that the Constitution is not nearly long enough nor comprehensive nor sufficiently amendable as to embody the needs of fully describing a complex legal system for a modern, legalistic society of 300 million people. So the body interpreting it has developed a lengthy body of tradition and scholarship that at times bears little resemblance to the original document, if one was to attempt to jump straight from point A to point B.
But what would you replace the current system with? What alternative system can be guaranteed free of human error and subjectivity?