I don't want to send all of my coins to the same damn address. Why isn't Poloniex letting me generate new addresses to deposit in different transactions using different addresses? Fuck these guys if you can't.
What exchanges that have BCH listed will allow me to generate different deposit addresses? I want to dump all of my BCH for once, but I can't send it all on a single batch, I need different deposit addresses.
Nope. They update the deposit addresses when they want, how they want it. You essentially have 0 say in when it's done. There is definitely no refresh address button anywhere. On bittrex, i'm pretty sure that you are able to generate a new address each time you deposit something. There is a refresh address button at the bottom.
Why do you need to have multiple deposit addresses, though? As mjglqw pointed out, there is no benefit apart from privacy, which you're going to get less of anyways if you were to use an exchange to process your deposits.
But i wouldn't recommend using poloniex, even if they did offer the option to generate new addresses. They have lots of issues.