Ah yes, the famously objective field of economics.
> Skilled workers have long had historical import...
Value, import(ance); potatoe, potartoe.
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.
If you‘d have chosen a burger flipper and an aeronautical engineer or a surgeon, I‘d have agreed with you.
Unless we're talking about really high end burgers, you can take almost anyone off the street and train them to flip burger patties within a day. They might not willingly do it on account of it being boring/tiring/poorly paid work, but it's not exactly hard to learn either. I doubt you can do the same for an accountant, unless your idea of an accountant is something like "manually copying entries into a ledger". Even teaching excel to someone who hasn't used excel ever, to a capacity where they can do meaningful financial reporting probably can't be done within a day.
On an absolute scale, comparing skills of burger flippers, accountants, aeronautical engineers and surgeons, the first two basically lump together.
I look at skill gap more in terms of „how hard is it to completely automate/autonomize this job“. Which is fiercely easy both for the burger flipper and the accountant, yet a bit harder (though not impossible) for the other two.