Why don't you charge a percentage of my card's value?
In short: Because a fee that grows with the value would give me a reason to push the value up. My fee is the same whatever I conclude, so the only thing the number reflects is the evidence.
Percentage fees are common in the hobby: consignment, auctions and some "appraisals" offered by people who also want to buy the card. Each one gives the person naming the value a stake in the answer.
Professional appraisal standards treat a fee contingent on the value or the conclusion as a conflict, and I do too. My engagement terms say it plainly: fees are never a percentage of the value of the property, and never contingent on a conclusion. That rule, together with the fact that I never buy or sell cards, is what makes the report independent.