The harm to society is also fixed, so charging a % of profits is a strange way to tax. Think of degree inflation as being a form of pollution.
Now think directly about pollution taxes. Emitting 1kg of pollution to create an iPod is not a bad thing - iPods are more valuable than having 1kg less pollution in the air. Emitting 1kg of pollution to make a sandwich is bad, however, since the value of a sandwich is much lower than 1kg less pollution. The end goal is to pollute only while making iPods, not sandwiches.
Charging as a % of profits or revenues would not create this incentive.
Similarly, the goal of an education tax is to create a disincentive for acquiring a degree for people who won't gain a lot from the degree.
"The harm to society is also fixed". No it scales with the amount of productivity lost during that time period. A football player that get's a masters before going to the NFL has a greater cost and a lower benefit than a teacher that get's a masters before teaching high-school English.
Pollution has a cost and production has a benefit. If $BENEFIT - $COST > 0, we want more pollution.
The problem is that since pollution is an external cost, the producer/consumer has no incentive to accurately make this calculation. As long as $BENEFIT > 0, the producer/consumer will pollute, and society will pay $COST.
The point of the Pigouvian tax is to give the producer/consumer an incentive to make this calculation correctly, and to compensate the rest of society for the costs they impose.
Now think directly about pollution taxes. Emitting 1kg of pollution to create an iPod is not a bad thing - iPods are more valuable than having 1kg less pollution in the air. Emitting 1kg of pollution to make a sandwich is bad, however, since the value of a sandwich is much lower than 1kg less pollution. The end goal is to pollute only while making iPods, not sandwiches.
Charging as a % of profits or revenues would not create this incentive.
Similarly, the goal of an education tax is to create a disincentive for acquiring a degree for people who won't gain a lot from the degree.