I think the same essential abuses that exist with debt exist here, so time-limitation (say equity stops yielding returns after 15-20 years, and can be discharged by bankruptcy) is important.

Yeah, so in the examples I assumed a 20yr duration. Note that student loan debt is currently not able to be discharged through bankruptcy though.

I worry about abuses when the equity stake is high. If you're a mentor, and your investment decides they don't really want to prioritize income maximization, what will you do?

Take a loss? Investors are used to small parts of their portfolio going badly. Obviously they'd prefer this not to happen. (Also you could limit the size of the equity stake).

Would the way to optimize returns involve hiring those you've invested in yourself (or arranging some convenient swap, if such direct employment is forbidden), and perhaps result in a system that looks either nepotistic or like indentured servitude?

My suspicion suggests not. What are the odds that the people who represent the most attractive investment (at current rates) also represent the best employees for your business? In general business in the US has been moving increasingly towards outsourcing over time - for example, few businesses own their property any more - and I would expect this to be the same.