I think there's an upper limit to the quality of entrepreneurial mentorship you can give, mostly as a function of (1) the mentors and (2) the mentor-entrepreneur ratio. Right now, YC invests in roughly $20k/company * 60 companies/batch * 2 batches/year = $2.4M per year. If they were forced to invest 50-100x that in a year, it'd be really hard to find 50-100x more mentors on the same level as the existing ones.
If a pension fund wanted to invest $250m in YC, they'd have to scale up by so much I doubt it would work the same.