The paradox is that as long as it's difficult to become in charge, only the really ambitious people will get there, and these generally aren't the people who'll serve others. Back to the lottery system?

If we move ownership from boards of investors to the people who work at a company, and make leadership democratically elected, such as in a co-op, things work out a little better. Yeah, ambitious people will still raise to the top, but their incentives will be to make the company better, not necessarily more profitable.

Ok, let's assume for the sake of discussion that co-ops are better in every way, what then? Should we just require all shareholders to be employed full-time at the company (effectively eliminating the stock market), or just the leadership?

For a co-op to work, every employee (And often, every customer, though that's not necessary) gets one vote. They become the shareholders. Yes, this means that company in particular wouldn't have stock with voting shares, but that doesn't mean it can't have a stock market. For instance: There are other companies.

>There are other companies.

Oh, but that's the thing, obviously there already are co-ops; my impression was that you wanted all companies to be co-ops.