Because they risk a "fiat loss" (i.e. "real money").

So if they have ended up on the wrong side of a fork they will actually go bankrupt.

I doubt any exchange is going to really want to "brave this" (so they will all just shutdown until a resolution happens).

Let's see if the exchanges are really going to publicly state that they will work on a fork (I very much doubt that any of them will do so).