How to scale down parallel complexity results to constantly many cores?
If you assume that the number of processors is bounded by a constant, then you are right that a problem being in NC does not mean much in practice.  Since any algorithm on a PRAM with k processors and t parallel time can be simulated with a single-processor RAM in O(kt) time, the parallel time and the sequential time can differ only by a constant factor if k is a constant.

However, if you assume that you can prepare a computer with more processors as the input size grows, then a problem being in NC means that as long as you can prepare more processors, running time will be “very short” or, more precisely, polylogarithmic in the input size.  If you think that this assumption is unrealistic, compare it to the assumption of unbounded memory: actual computers have only finite amount of space, but in the study of algorithms and complexity, we almost always assume that a computational device does not have a constant upper bound on space.  In practice, this means that we can prepare a computer with more memory as the input size grows, which is how we usually use computers in the real world.  NC models an analogous situation in parallel computation.