My coworker spent 30 minutes trying to find another way to contact a vendor after I told her the easiest way to order the thing she needed was just to call and it would take 2 minutes. I hate calling too, but that's just dumb. Or maybe I just like efficiency more than I hate the phone.
I mean, if there's a fully functional way to order online, why would you call? I just prefer a phone call when something would take paragraphs to explain or if there really isn't an easy way to do something via a website/email.
Some of the online ordering services are sneaky and bake their fee into the prices of the items you order, so it's not even clear that you pay extra. My despise of that practice motivates me to call in my orders.