Most institutional money requires that you use a broker who has substantial assets that can be used as a cushion. You wouldn't put $1B at a firm with $40M in assets for example. So, while I've seen IB accounts around $50M it's always been a collection of retail investors.
There are only a handful of brokers/clearers that are ever allowed.
Also, the great majority of places, especially really big places, would never write direct to an exchange. Most big business still done over the phone looking at Bloomberg.
It's hard to keep a sense of scale. Like how small GETCO is in terms of assets compared to an average size traditional fund. We tend to see trading as a large world but it is very small compared to the rest of the financial industry.