Same here about express cash outs. I've had a couple of players literally ordering an Uber right when they announced they were cashing out. I told them not to do so and to wait to have the money in their hands before ordering an Uber (I live in a popular area in a big city, so you can get a car to you within 3 minutes of ordering).
I think this is a mistake on their part and not yours (the host/director), as indeed you do not want to screw up any cash out amounts, sometimes you miscount one $20 chip and it's money you'll spend from your own pocket.
What I do is ask them to count their chips, tell me how much it is in total and then I count the chips myself and make sure to note it down on my sheet. Crossing information is the way to go. It's happened to me once that a player told me a number that was like $30 short of what it really was, so it's also in their interest to wait 3-4 minutes rather than running off.