If there's a rising proportion of mega-rich people in any given study, this could introduce significant sampling biases. Ethnicity, diet, lifestyle, gender - it all factors in and will have to be controlled for appropriately.
Another concern is that this could introduce incentives into the eco-system that detract from the primary goal that is to obtain a drug that would be effective for as many people as possible (setting aside drugs with specificity as a goal for a moment).
Imagine there's a drug A that happens to show very promising results on caucasians but not so much for africans, and a drug B that has more general effectiveness (hackneyed I know, but please bear with me). While a more impartial set of trials might have wound up selecting drug B (albeit after some passage of time), it's now possible drug A could get fast-tracked to market by virtue of being awash with funding from affluent volunteers while drug B never generates enough monetary interest to make it.