We know how to match our effective field theory of protons and neutrons in nuclei to QCD observables. This project has been under way for 20 years. Expect major breakthroughs as the exascale machines mature. If we match our EFTs to QCD calculations then there would be no additional parameters fit to data, and our intellectual edifice will have quantitative predictivity from fundamental particles to neutron stars. It's hard. Nobody promised that physics should be easy.
That means that such computations have little, if any, practical importance.
With the current QCD, it is not possible to compute the ratio between the mass of the neutron and the mass of a proton with a useful precision. The mass ratio between the proton and the electron or the mass ratios between light nuclei or their magnetic moments are even less possible to compute.
QCD would become a useful theory only when it would be possible to compute things like the probability of fusion of light nuclei with a precision good enough to eliminate the need to measure such values experimentally.
QCD would need revolutionary improvements to achieve such goals.
Supercomputers are not enough for a progress in this domain. Different solving methods must be discovered.
> QCD would need revolutionary improvements to achieve such goals.
Make the computers 10x faster and the algorithms / libraries 10x faster and all the things you wish for are within reach. Much more plausible than _overthrowing the standard model with something that offers easier calculations_.
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.
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.
Even if we suppose that the standard model is completely correct, it does not allow the computation of the majority of the useful physical quantities.
What is needed is a model that would be able to compute all the physical quantities that are important in practice, e.g. the masses of all hadrons and of all atomic nuclei, also their magnetic moments, the energies of their excited states, the energies of the excited states of the atoms and of the ions, and so on, starting from the properties of the elementary particles and of their interactions.
Despite the huge progresses which have happened in experimental physics, we are now no closer of having a useful theory able to compute what we need ab initio, than we were exactly one hundred years ago, before the most influential work in quantum physics was published by de Broglie, Schroedinger, Heisenberg, Dirac, Born et al (from the point of view of the computable values, the Dirac theory of the hydrogen atom was only a minor improvement over what could be done using the Wilson-Sommerfeld quantization condition from 1915 and the more complex systems remained uncomputable; the quantum field theory improved a little the precision of some previously computable values, but only very few other additional quantities became computable ab initio).
All the useful applied physics, e.g. the theory of the semiconductor devices, or theory of the lasers, and any other theory used to design real devices, do not have any use for the standard model, but they use various empirical mathematical models, which contain lots of parameters that are determined experimentally, in order to match the predictions of those models with the experiments.