Re: Speculation!!!! It's worse than that...
Firstly, these 20k are not brokerage fees, they are the trading P&L and if a brokerage house is doing what you described in your example, that profit belongs to the principal client, not to the brokers.
Quite separately, the broker will charge the client its fee for doing the trades - those will be the brokerage fees. If there is very little or no benefit or necessity for the client to do these trades but the broker is doing them anyway, this is known as "churning" and is a form of fraud or breach of fiduciary duty, but that's a whole different story...
Back to your example - let's assume that the broker is acting in good faith and has found an arbitrage opportunity which is likely to benefit his client. Let's also assume for simplicity that the best offer in Chicago and the best bid in NY are precisely 1 million MSFT shares.
When the broker buys MSFT shares in Chicago at 39.67 the exchange fills the order and all offers at that price are taken up, the next best offer is 36.68. In New York, the broker similarly sells the million shares 36.69 and the new best bid is now also 36.68.
By making his arbitrage trade the broker caused the two markets to synchronise.
You call it "coin flipping" but it is exactly the opposite. It's known as "risk-free" transaction and whenever an opportunity for a risk-free profit exists it is a sign of inefficiency in the market. After that trade there is no more opportunity for a risk-free profit and therefore the inefficiency is gone (for now).
If, however, the broker were to just buy some MSFT shares for the client in the hope that eventually its value will rise - that would have been coin flipping, aka speculation. But, oh, wait - the ultra-leftist public here calls this an "investment", go figure...