These special values are too few to matter for practical applications and they apply only to exceedingly simple systems, e.g. a single free lepton or a single pair of interacting elementary particles.
The practical value of QED is null. By far the greatest success of QED is what you have mentioned, i.e. that it explains why g_e is not exactly 2, but it is slightly different. This fact could not be explained by the Dirac theory. However, we already knew the value of g_e through experiments. Having an explanation for our peace of mind is good, but this cannot help us design anything.
For example, it would have been enormously helpful if there would have existed any method to compute accurately the frequencies and various other properties of the spectral lines of the atoms and ions.
This would have allowed e.g. to find through computation optimal substances for applications like lasers and atomic clocks.
Because there exists no such method, the advances continue to be done only by discovering through experiments new better spectral transitions of certain atoms or ions.
This qualitative understanding has been very helpful as a guidance in the development of various approximate methods used for the modeling of the systems that are too complex to be computable ab initio, e.g. atomic nuclei, atoms with many electrons, molecules, semiconductors, superconductors and so on.
Nevertheless, while the qualitative understanding was improved by the more recent theories, they remain useless for obtaining quantitative results.
All physical systems that are interesting are too complex to be computable ab initio, so in order to predict anything about them, wild approximations must be used, which are different for every physical system. There are no universal rules about how to develop such approximations.
If an approximation method is found, which after measuring experimentally the values of various parameters allows a model to predict other experiments with sufficient precision, then good. If not, there is no way to know if some other acceptable method can be found, and how to search for it.