From my knowledge there is no day bitcoin is replacing paper money and it's not created to replace paper (fiat) neither was it created to compete with fiat. Bitcoin is created to be a supporter to fiat where fiat payment can't scale through bitcoin will solve the problem, for instance you can be at your home to transacts some billions of dollars through Bitcoin without have to go queue in bank where they would start asking some silly questions about huge amount you are sending out to people, also in bank there are always some certain amount you can send per day or months but with bitcoin you won't experience those barriers.