Why is trading behaviour so similar across all (mainstream) exchanges?
You, as in the collective you that makes up the trading market.
Whenever the price differs enough between two exchanges, a trader who has an account (and funds) on both can profit by selling on the cheaper one, selling on the more expensive one, and then possibly transferring fiat/BTC to compensate. Of course, there are trading/withdrawal/transfer fees involved in all of these, but if the rates differ enough, it will at some point inevitably be worth it. This is called arbitrage.
Sophisticated traders likely keep funds specifically spread across exchanges to take advantage of this, and may have automated trading bots that trigger buy/sell orders whenever arbitrage opportunities arise.
The result of people exploiting arbitrage is that the price starts to balance out across exchanges.