Sure, it's easy to set up online bill pay through the bank - which lets me know that the money's been deducted from my account. What it DOESN'T tell me is that the money has been RECEIVED by the person I'm paying (which is actually something I'm dealing with right now - two due to the post office, and one was an online payment). The way I do it now, I know, I can track, and I can avoid late fees (and overdraft charges). Autodraft? Absolutely NOT. My bank's online bill pay? Not if you paid me.
I guess working in banking for the last 9 years has soured me on it, but not without good reason.
I never believed in it until the last year or so. Things have improved a lot. I've had no problems whatsoever when handling personal banking online, at work as an accountant/bookkeeper for a small business, and with my own small business of sorts at night and on weekends as a gigging musician. I do most of it through PNC and Chase now, and Chase has been spot on every time (1 day or less to deliver payment). I've had one minor slip up with PNC and they're a bit slower with eChecks, but we're talking one slip up after thousands of transactions for a small business. You'll likely have those one way or another anyways, and at least we have a clear "digital confirmation" trail to back us up now.
Maybe you should just find a new bank. Everyone talks crap about Chase, but they've always been good about waiving fees for me when I was just a high school kid, then a poor college kid, a poor post-college kid and then a slightly more stable young-adult. They've promptly corrected any errors that have come up and waived numerous overdraft fees for me when I was younger and not aware of linking my checking and savings account. And with Chase, I can manage ALL of my accounts and pay all of my bills in one app on my iPhone or iPad. I don't even need to go to the website anymore. I can see everything from one central location and I don't need to worry about having credit card data everywhere. There are no fees, and it's amazingly simple. And again, to be totally clear, I have literally had to pay just one, as in 1, $10 fee to chase one time when I set up and managed an account incorrectly. They probably would've waived it if I called, but it was well-documented upon basic inspection and clearly my fault so I didn't bother.
Also, I've found again and again that just because a bank has fees listed out on paper, they don't always get enforced. I take a few minutes to sit down with a banker once a year or so to go over all of my accounts and any changes, and should anything odd arise that might lead to a fee, it's been pretty easy to get the fee waived. I oftentimes don't even have to ask; they just do it as I'm sitting there. I can't speak from an internal perspective, but I have to imagine that they're more willing to help out customers who take initiative and seek out some semblance of a relationship because A) on some level they might trust those customers a bit more and B) they're going to want to maintain that relationship to keep the customer with the bank.
So I always tell people, if you don't have a pattern of screwing up, if you take some initiative and if you're friendly and polite, things can be pretty smooth dealing with even the biggest of banks. It's obviously not a hard fast rule, but it's worked for me and many of my friends who took the advice.