That's just playing with words. Putting Gordon Ramsay in the same bucket as "burger flipper" makes as much sense as putting Linus Torvalds in the same bucket as "keyboard monkey".
Why are you pivoting to "value"? The original discussion was about skilled vs unskilled labor and whether that assessment is subjective vs objective. You might think that accountants are useless paper pushers whereas burger flippers are Hard Working People That Get Actual Things Done™, but that's orthogonal to how much skill[1] is needed to flip burgers vs be an accountant.
So you're trying to derail the discussion to something about "value", because the page I linked about "skill" has a passage about how skilled laborers were historically important to the economy? What does this have to do with the subjectivity/objectivity of "underpaid", "unfair wages", "unskilled labor", or whether a burger flipper is more "skilled" than an accountant? As I said earlier, even if you think that accountants are useless paper pushers, the fact that they're pushing papers in a very specific way that takes years to learn, makes them more skilled.
First I'm pivoting now I'm trying to derail, when all I've done is answer you question; but to make it plain: yes, it's subjective. How else are certain skills valued more that others? There's no objective measurement to these. Comparing the skills of one disapline to another doesn't work, like apple to oranges.
The objective measurement for "skill" is how much training/experience/talent is required to carry out a particular job. Sure, there might be some fuzziness/ambiguity to this, and there's various degrees of freedom to how you compute a "skill score" or whatever (eg. what's more skilled an accountant or an auditor?), but it's hard to argue that a burger flipper is more skilled than an accountant. You can make the argument that the value of a burger flipper vs an accountant is subjective, but that's irrespective of the skill required.
Whether someone is getting "underpaid" or a "fair wage" on the other hand is entirely subjective, and you can come to whatever conclusion you want depending on your politics. On one side of the spectrum you could argue any sort of situation where the employer is capturing surplus value from the employee is inherently exploitative[1] and therefore "underpaid" and a "unfair wage". On the other end of the spectrum you argue that supply and demand curves are the ultimate arbiter of what's "fair", and any wage that is determined by the free market can't by "underpaid" or "unfair" by definition.