If you're interested the service is called the Customer Information Manager. You can use it to store any secure data that you'd rather not be responsible for. I've used it to great success.
My main reason for my love affair with authorize.net? Recurring billing. They nailed it.
For most people, they aren't (and don't want to be) experts in payment processing. Improving their product moves the needle by more than 1% for the same (or less) effort than spending time on payment processing.
Stripe is an amazing service and their founders are amazing people. I wish I could blow them, but they probably wouldn't even let me b/c the VCs are already all over that. On the other hand, for people who enjoy saving money, becoming PCI compliant and saving 1% + trans fees is another alternative and there are numerous tutorials available to help anyone do that within a few hours even if you are severely autistic.