It's pretty hard not to though. You rely on your hosting provider for service and probably on a multitude of software services too. Of course you have to weigh the value of each further point of failure in your setup, but it's a tradeoff and may well be worth it.
Valid point. Still - that doesn't categorically make it a bad choice. It just weighs a bit heavier on the con side. There are some positive effects of that dependency as well (User trust and convenience).