“Will the Republicans embrace this plan?
Almost certainly not.
Would Democrats embrace this plan? Almost certainly not.
The core of what you describe is what health insurance USED to be. You had “health insurance” for broken bones, infections, etc… and “major medical” coverage for things like major heart or brain surgery. Oh, and “routine care” (i.e. physicals, annual exams, etc…) was all paid for out of pocket.
But over the years the States have expanded minimum coverage requirements to cover all sorts of things and people cry if they have to pay a $20 co-pay for an annual physical. Add in the whole “Rise of the HMOs” during the 1970s and the change from health insurance being provided as an employment benefit meant to retain employees to a mandated requirement… yup. We’ve got a mess.
Sorry but health care isn’t getting “fixed” until employers are completely removed form the picture and the actual care providers, pharma and medical device manufacturers are included in the regulatory scheme.