Because if you have a death in the family, on vacation with your kids, or something like that your Amex bill may be the furthest thing from your mind. That and I'm not so paranoid as to think what American Express is going to do if they have access to take my minimum payment from my checking account. It's a good way to be sure your minimum payment won't be overlooked or forgotten.
Just do what I do, Online monitoring for all of them... I have my website set up as a bookmark with all the links of my credit cards so I can check them whenever I want.
What I do, as well. Creat a bookmarked folder with all "online banking credit card sites," and check periodically with seemless integration through icloud (or, any cloud computing environment).
Can access from anywhere and at anytime. So easy these days to keep track of almost an infinite amount of things simultaneously.