I don't think you will find a reference showing that LDAs are better than GGAs for computing elastic constants. More specifically, I don't think a paper could reasonably offer an explanation of why LDA does better than GGA for any specific case.
In principle, a GGA is more physically consistent than an LDA, as we know that the true exchange-correlation functional of DFT should depend on the gradient of the density. In practice, DFT functionals are typically parameterized to minimize errors in the energy for test set of molecules/compounds. Due to the approximate nature of the functional used in practice, there will always be cases where the "inferior" functional does better simply due to coincidental cancellation of error. There might be classes of compounds/problems where the source of this cancellation can be determined and a rigorous explanation of the good performance of the "inferior" functional can be formulated, but this is rare and generally very challenging.
You are looking at a small selection of materials with fairly different properties (e.g. different crystal structure), so its unlikely that there is some clear, common factor that is making LDA better for these cases. A paper in the Journal of Computational Material Science found that for cubic crystal, there were cases where LDA produced better elastic constants and there were cases where it was much worse than GGA.
- Jamal, M.; Jalali Asadabadi, S.; Ahmad, I.; Rahnamaye Aliabad, H. Elastic constants of cubic crystals. Computational Materials Science 2014, 95, 592–599. DOI: 10.1016/j.commatsci.2014.08.027.