Not a good idea. If you choose to only use bank cards or credit cards and only order items online with the card, you open yourself up to fraud possibilities.
If someone or company claims you did not pay a bill and you had paid with a paper check a trail has been created that is far more extensive than what a credit card on your statement reveals.
A canceled check has a great deal of information on the back of it. In order for the receiver of that check, whether an individual or business, to get their money they must endorse it. They will endorse it by using either a written endorsement or a stamp. Their bank will also use a stamp to show when they received and posted in their depositor’s account. The stamp shows that they did get it and were paid.