I've submitted tax returns for last 5 years without ever printing anything at all. I don't think you need any printed paper - in theory, it can be done with zero paper at all, in practice many places send you printed forms (though I believe they have an option to choose electronic delivery, many of them do not support it) but you could do without printing anything yourself if you want to.

Maybe if the tax return is really complex and most of the software can not handle it you'd have to go back to paper. But for vast number of Americans, tax returns are simple enough.