Pull systems are THE WORST because you're putting 100% trust in the party you've given your account number to. I have multiple friends who have had various parties withdraw payments for loans in excess of what they were supposed to withdraw which put them in a serious financial predicament.

One in particular set all his bills up on auto-pay such that he didn't have to pay terribly close attention. His government-backed student loan payment took out something like 5x what it was supposed to and as a result he missed two months worth of payments (again because he didn't check regularly) and got quite a few other companies rather pissed off. And he had no recourse with the student loan folks.

After hearing about that kind of bullshit (I too am mostly setup for auto-pay) I got a second account with a totally separate bank which I occasionally deposit a few grand in for the companies that won't accept credit card payment for their services. This way even if one of them goes rogue and siphons the account dry they can't take me for more much more than is in the account. It doesn't protect me against someone going after my other accounts using judicial means, but it does provide a substantially higher barrier and gives me some peace of mind.