100% agreed, another reason for the Index
Although some will be able to take advantage with arbitrage, the transaction times of bitcoin end up helping the exchanges. Most people don't have enough funds spread through multiple exchanges. Think of this as a sort of dispersed "pump" or something.
Admittedly, we see this sort of thing with other exchanges dealing in alts (where there are fairly large spreads between exchanges). Although, relative illiquidity is the culprit in those scenarios.
You're partially right in that large spreads would help them get away with it (although that is also self defeating).
But it doesn't matter what "most people" do. Even 1 competent arbitrager will take money from exchanges trying to set prices, which is enough to discourage it.
But in the case that exchanges are okay with oscillating funds (still a type of price fixing), unless the person (or people) doing arbitrage has around the same amount of liquid money as the exchanges, the exchanges can still take advantage.