Ask PG: Why not take YC public like Berkshire Hathaway?

Why not take Y Combinator public like Warren Buffet's Berkshire Hathaway? If you did, everybody could invest in the next big tech hits indirectly. Also, by investing in YC everybody could enjoy the diversified risk versus investing in much more volatile individual companies.

Have you considered taking Y Combinator public? If not, what are the compelling reasons to avoid that course of action?