I wish I knew better how to use them for these coding problems, because I agree with GP they're underutilized.
But I think if you have constraint problem, that has an efficient algorithm, but chokes a general constraint solver, that should be treated as a bug in the solver. It means that the solver uses bad heuristics, somewhere.
I'm pretty sure that due to Rice's theorem, etc., any finite set of heuristics will always miss some constraint problems that have an efficient solution. There's very rarely a silver bullet when it comes to generic algorithms.