Professors historically were prohibited from relationships with students because it creates the appearance (and high likelihood) of favoritism. And it probably pisses parents off a lot because the age difference seems creepy.
"Power" is a relatively new argument. These days the student has the power to utterly destroy the professor. The professor has at best the charismatic "power" equivalent to any number of smooth pickup artists occupying college dorms, of getting a temporary good time.
I think it's still a fair question. The money is intended to be an incentive. If the trial is ethical and has a positive risk benefit ratio, there is no harm from coercion.
Okay, but what if a person sincerely does not want to participate in a medical trial? But then when he sees the dollar figure, he thinks "well, shit, I hate doing this, but I can't afford to turn that much money down."
Same reason we don't allow the purchase of kidneys, and the same reason we think it's unethical for a millionaire with a tophat and a monocle to offer two homeless guys a wad of money to the winner if they fight each other. Sure, it's an adult making a decision of their own free will- but it's obviously unethical.
Why shouldn't college professors sleep with their students? How does the relationship become less informed or less consensual? The answer is power.
Money is power, and too large of a power imbalance corrupts a relationship. Money is pressure, and too much pressure is coercive.