Faster withdrawals for users.
Easier way to get hold of Bitcoin (your money is already in your account awaiting withdrawal, so you can avoid the multiple hoops you'd usually jump through with exchanges etc).
It makes sense! Bitcoin is the internet of money. It seems like a logical feature for withdrawing money from websites.
Probably easier to process by the company initiating the withdrawal?
The withdrawal could be processed via an exchange API (the site auto-buys the equivalent amount of BTC from the exchange and sends it to the withdrawal address for a fee).
I think the biggest use case for this would be gambling sites, they're always the hardest to get your money out of. But then there's merchant accounts like PayPal, affiliate networks, trading platforms, heck even bank accounts.
I'd personally always use this withdrawal option if it was there. Anyone who has heard of Bitcoin but finds it too difficult to buy could also easily get their hands on some with this option.
Taking this one step further… imagine a time when Bitcoin wallets are securely built in to your web browser, and you can simply withdraw straight to your browser from one site, then go spending on another site. Never need to touch a credit card again!