Their exact cut is generally a balance between the risk, reward, and ability of the venture to happen without them.
Risking the largest absolute financial input is not equivalent to having the highest risk unless you exclude all human value, and consider a dollar to be of equal value to all people.
Bigger musicians will fetch high prices and in some cases, take on the financial "risk" (almost none since they're a superstar) themselves.
Also, its not like a single bad song is going to ruin a career. Clearly you haven't heard an album from the front to the back if you think that.
If the musician was able to provide enough capital/resources on their own by risking their entire livelihood they'd have no need for an investor and could take the entire profits of the venture for themselves.
I'm not making a moral judgement here, I'm just saying that it's a fairly straight forward logic as to why people who "only contributed financing get a bigger cut". The OP is wrong to claim they get a bigger cut because they're already rich, they get a bigger cut because they're risking more capital in the venture. It is secondary that them being rich means they have more capital available to take risks.