It's called arbitrage trading. Here's why all the prices aren't the same:
-There's a "spread" on most exchanges, which is the difference between the buy and sell prices.
-Some exchanges have high fees (e.g. Coinbase)
-Some exchanges are dysfunctional (Bitfinex, BTC-E, Chinese exchanges), and some exchanges are also extremely shady/annoying when you move large amounts (BTC-E, Poloniex and more).
Overall doing arbitrage with several exchanges can get very hard. There are some minor opportunities with the extreme price fluctuations that go on, but they're gone very fast. I don't recommend you get involved unless you know what you're doing or you can trade with foreign exchanges (like South Korea).
Same here, I once tried arbitrage trading and it is not actually a good recommendation to trade at multiple exchanges but if you have lots of capital for the coins you are buying then it'll work for you. But there are some traders who transfer the coins they bought at this certain site to another site because they bought it low and the tendency is you'll receive the transfer so late because of the traffic blockchain. But there are also some traders that works for them though.