For example, though - if you took BTC/USD on bitmex (which doesn't support USD deposits/withdrawals, instead uses a price pegging system), and BTC/USD on bitfinex, which uses USDT, arbitrage is not possible, because there's no way to exchange USD between exchanges, so market structure does matter in this case.
I'm just wondering what the constraints are? Is it simply the ability to deposit/withdraw the base/quote currencies on both exchanges?
The only constraints that are there are the constraints you are putting on yourself and what your goal happens to be. For example, you are assuming that in order to arbitrage you must move your coin from one exchange to another - you would be better served to simply worry about the outcome. If you buy low and sell high, why does it matter if you combine the coin? You have ownership of the low cost coin and you sold the higher cost coin.You do not need to exchange USD or BTC between exchanges, simply having more BTC or USD in total, accross all platforms should be your goal. Collectivize your portfolio, broaden it and diversify, do not try to lump it all in one place as this is where you are losing profit.