Innumerable small businesses depend on payment by cheque, not to mention private transactions. People do not want to carry large amounts of cash. Surely this move would be a step backwards, and make life considerably less convenient for almost everybody.
If the justification is that of saving paper, this would be ridiculous when you consider how much more paper is wasted in other ways which are not useful in any way, such as excessive packaging, and in any case, used cheques can be recycled like other paper.
The human interaction of an agreement and a trust between two parties by face-to-face transactions can never be replaced by using the internet.