The idea with taxing the credentialed position is that it provides some incentive to not attach a credential to positions.
You should ask the parent, not me. I do not advocate taxing getting an education, whether you do it directly on indirectly.
Besides, in either case, such a tax would infringe on free speech.
The parent of your post did not propose what you did, your idea has poor incentives for people seeking education and can be expected to have 0 influence on employers. Their idea has little impact on incentives for individuals seeking education and can be expected to encourage employers to consider the necessity of an educational requirement for a given job.
Do you really see them as equivalently arbitrary hurdles to employment?
(Unless the idea is that taxes should be based on whether or not a job posting requires a degree. But that would be silly, because employers could omit the education requirement from the job posting but still hire the best candidates, or have the need for a credential be taken for granted via codewords like "engineer.")
The incentives for the roles where the credential is meaningless change because the employer can choose not to pay the tax (by removing the requirement for the credential). Under your proposal the employee can't.
Which would be illegal, and carry a penalty. Unless they choose not to hire someone with an education, in which case, they didn't need the person to have that costly skill.
More: But I see that I've misunderstood what you initially proposed. It doesn't make any sense to me to tax the education, I'm not sure taxing the (credentialed) position makes sense, but at least it provides cromulent incentives.