Can an arbitrager not simply hold both BTC and cash on multiple exchanges at once? When a price difference swings one way, sell on one exchange and buy on the other, without worrying about transferring anything between exchanges. When the price difference swings the other way, do it the other way round.
If price differences average in both directions over time, you shouldn't run short of either BTC or cash but you will make a profit.
If price difference average in one particular direction, you can notice that trend and transfer across in advance.
An initial investment is required, but that is true of any arbitraging activity.
I had assumed that this is what arbitragers have always done.