I would agree somewhat. A lot of ivy grads trade their own accounts/start their own funds. Generally speaking though, you need a degree from a top school (if not, a notch below those you mentioned such as schools like UMich, NYU, etc.) in order to get anywhere near an institutional trading platform. The risk is way too high to hand unlimited BP to n00bs. I agree about the other 3. There are different types of firms that cater to different people. I would go out on a limb and say top traders at level 2 are making just as much as the big guys on the top level.
The first 2 levels require Higher Education degrees: most recommended (math, computer science). Those that work for goldman, ubs, or others in level 1, last 1-2 years minimum an average before heading down to level 2 (higher bracket). From level 2, they'll stay there for an average 3-5 years minimum Those begin trading in the ghettos level, will not make it. Those begin trading in the LEGIT lower bracket level, have a better chance of making it in the "profit making status" vs those that begin the ghettos level.
The only way to get into those top level schools is an SAT score above 2000, a 4.0 GPA and lots of other activities like being able to play the piano. Showing some serious talent.
Mod, where are some of the recent posts? As long as posts that are not insulting, you should not remove them.