Wave:
So my claim is that GR fully explains the property we observe as mass with the one missing point that GR does not explain how mass curves spacetime.
that's an objective, for sure, but hasn't been achieved yet. The Higgs fields, so many of them I can't keep track, attempt to provide a mechanism for mass...But like many other components of the standard model, these Higgs fields are manual insertions individually tailored with the specific properties needed to provide different particles with the observed mass. A nice interim step, but hardly a comphrehensive theory.
I happen to be reading right now Alan Guth's 'The Inflationary Universe' and he discusses a few Higgs fields in Chapter 10/11. As an example, three Higgs fields are used to describe [construct] magnetic monopoles. So Guth talks about how he tried to avoid the magnetic monopole problem in a theory of inflation, that is, the fact that there could be many, but we observe none. How do we avoid them?
He realized if he could delay a phase transition in inflationary expansion#, horizons would increase in size and magnetic monopoles would disappear...be smeared out of existence, hence his reliance on a Higgs field with a false [temporary] vacuum...the old 'Mexican hat' energy density profile.
Sidney Coleman's 1977 paper THE FATE OF THE FALSE VACUUM describes "The process by which the Higgs fields of the false vacuum can tunnel thorugh the energy barrier..and Coleman's work was a big help to Guth.
Voila: when you know the physical characteristics required, you can invent mathematics to produce them and glue them into whatever model you'd like. It's not like all this stuff is available via first principles. How could Higgs fields, if they exist at all[+], not be related to gravity when both a related to mass...but that link apparently remains a mystery as already noted in a prior post.
# Guth points out what he thought he 'discovered' about inflation turned out to be in a 1925 Lemaitre paper from MIT that he knew nothing about...the de Sitter solution to Einstein's field equations...but apparently Guth coined the term INFLATION as part of his research.
+ I am referring to the existence of multiple Higgs fields not whatever might have be identifiey at CERN...