I agree, it's not perfect - just a useful abstraction. Just the same as arbitrary thresholds for correlation or a p<0.05 significance level - often you lose information but gain insight. From personal experience I've seen MST's map out underlying structures that validate classical chemical kinetics of a system in a logical path: something that would not have been apparent in ordinary thresh-holding approaches
Basically IMO it's good to use all of these techniques together to get a good picture of your system. In the end the greatest limitation is our human cognition to interpret the results, which frankly needs all the help it can get.
Nice article. You could consider maximum spanning trees as a way to prune your correlation graph; they are very effective at suggesting underlying structure or kinetics of a system. Just use the minimum spanning tree algorithm with the inverse of your correlation.
Another approach is to use PCA on the adjacency matrix. This can generate interesting clusters based on the latent variables. At the risk of self promotion I co-authored a paper on this technique which validated known pathways in a metabolic network
Basically IMO it's good to use all of these techniques together to get a good picture of your system. In the end the greatest limitation is our human cognition to interpret the results, which frankly needs all the help it can get.