I think the criteria they have is just about right. Real institutional traders are dealing with millions and millions of dollars and multi-million dollar accounts.
the candidates need to have a long track record of working very hard in very competitive environments and suceeding. They need to be the tops of the tops with strong math skills and also be personable to work with their clients.
They need to be able to take the pressure without burnout, and not have high turnover.
threfore Ivy league, top of class, young, sharp, and with internal referrals...is the way it needs to be.
lets be honest that the average individual trader (like those of us on this board) dont meet this criteria. that is why we do it for our own account...instead of with Goldman Sachs money.