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(And how you can't say who is better off, a person who experiences, x1y1z3, vs x2y2z1 vs x1y4z1.5)
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Actually I think that some forms of privilege not only can be quantified, but should. In fact, quantification is what allows us to determine whether a given social category is a form of privilege or oppression, and this has real consequences.
Examples:
When people want to deny trans women access to women's resources like emergency shelters, they usually argue that trans women have too much male privilege. Without quantification, this can only be contested through an ideological argument that ultimately has no measure of falsifiability (it can't be proven to be wrong) and thus is irresolvable. This then leads to a decades-long stalemate between the (thankfully increasingly rare) women's organizations with moderate to low resrouces and trans people with low to no resources. If, instead, we ask what the criteria are for admission to this shelter (limited income, risk of violence from partner, in society and in men's shelters) we can establish that trans and cis women both need to get into these things - actually, trans women, on average, need them more. Were the people trying to exclude trans folk to actually listen to this form of argument, access would improve and with it, quality of life.
Another example is the frequent claim in politics that indigenous people have it easy and clearly have a form of privilege over white people - due to band bursaries, reduced taxes and government programs. If one quantifies the very limited value of these (frequently slow) bursaries (which are limited to people with membership of a band that can afford them), the marginal gain from buying goods tax-free less the opportunity cost that comes from living on reserve (which is necessary to get these discounts), and the actual value of these government programs, and then if one compares it to the cash value of white employability, reduced police harassment and the average intergenerational wealth transfer, one can conclude that the average's individual's person's experience, it is actually the case being white that is a form of privilege versus being indigenous. This has policy implications. And it has numerous parallels in other discussions over equity measures.
While many incidents of privilege are still hard to quantify, the social categories through that determine when and how they occur often track with quality of life data, and from this, you ca get a picture of what's easier. This can allow apply within one form of privilege - for example, the 1965 book The Vertical Mosaic quantified different forms of racial privilege in Canada, and this ranking of racial ancestry versus life outcomes and political power still holds. From this, one can also state that, for example, all forms of neurodiversity (mild ASD vs Schizophrenia) are not equal burdens - and this too can be quantified, as is done with physical ability in the Paralympics.
Using this method, you actually can answer the questions above. You can do so holistically, or for each variable or combination thereof as experienced differently by two people of differing social situation. When the numbers are so close as to be swayed by small difference in interpretation, you can conclude that both can expect roughly equal but different outcomes. But when there is no reasonable equivalence, you can say who has it worse off in a given category (and the situations in which it has an effect), or overall.
