If you end up in a dispute with your phone company, you are putting yourself at their mercy. It's waaay easier to fight a charge you haven't paid yet, then to recover money you've already paid.
I've gone through hell because of this.
[edit] Oh, I guess you mean in the case of a regular payment of an uncertain amount, like a mobile phone bill. I use a pay-as-you-go plan where a direct debit takes a fixed amount out of my account each month, and if I overrun it then my phone stops working until I pay more. I'd definitely think twice before setting up a DD for a mobile phone contract.
On the other hand I know many people who like me do not use direct debit for "unpredictable" things like cellphone bills. Most other payments can be automated by standing orders, what sucks that even when your monthly phone bill is essentially constant you cannot do that as our cell operators generally assign distinct payment reference for each monthly bill.
Standard description : https://en.wikipedia.org/wiki/Short_Payment_Descriptor
One thing that fascinates me is contrast between european giro banking systems and ABO in particular (where account number is just an ID/address and has no security implications) and checking account based system used in US where everithing seems to be somewhat backwards from what would make sense.
As for paperlessness: I routinely pay my cellphone bills by scanning said QR code from computer screen.