I would hardly call it "solved".Your argument is based on ignorance of how sales tax/VAT codes work. Believe it or not, but tax people and businesses have been dealing with these issues for over a century now and they've mostly figured it out.
It is ostensibly a luxury for the well-off.
No, even for the well-off it is still a medicine.
Parmigiano Reggiano DOP aged 48 months is arguably a luxury, but generic parmesan cheese isn't.
In places where it matters, the sales tax codes can get as granular as they need to address this. They don't need a dedicated bureaucracy to make these determinations: it's either handled by the legislature or a very small team, since determinations like this are infrequent and don't require dedicated staff.
In this particular case: both DOP and regular generic parmesan are classified as foodstuffs by CA and neither would be subject to sales tax.
but it leaves much to be desired from a "fairness" perspective
Someone buying a budget car should be taxed less than someone buying a luxury car, regardless of the wealth or income of either buyer.
It's not like they buy 100x more luxury items because they make 100x more. Most of their money is spent on investments, not consumption.
Indirect taxes are not consumption taxes. They are transaction taxes, and investment transactions can be taxed under a sales tax, GST, or VAT regime. Some jurisdictions do tax investment transactions. In the U.S., taxing investment transactions has been proposed many many times over the past few decades. Wall Street have managed to beat off that proposal through profligate lobbying but every time the proposal pops up it gets more support...