What you describe is not arbitrage. Arbitrage would be buying stock on one exchange and selling it on another without knowing jack about the order book.
What I am describing is exactly arbitrage. There is not one order book, there are fourteen order books (one per exchange). When one order book gets cleared out, the arbitrageurs make a bet that the other order books will get cleared out as well, so they take on the position with the hope of now being long at the new bid, or short at the new ask. They do not know that the other books will get cleared out, because they don't know if you wanted e.g. all 22,000 Intel shares, or just 2,000 (which just so happened to clear out 3 exchanges, but not the others).
This is definitely a problem for large executions: you move the price before you are done with your whole "trade". This has always been a problem for executing orders larger than the current top-of-book. It is made worse because there are so many exchanges, but also because some of them are so darned fast that HFT systems can beat brokers' order routers. You could argue that there should be a delay in publishing market data to ensure that routers can compete. You could also argue that it doesn't make sense for fourteen exchanges to exist, with regulation that merely attempts to paper-over fundamental natural laws (simultaneity). But you can't argue that it is not arbitrage.