The short awnser is no.
Blockchain as is cannot be the back of cryptocurrencies in order for that to happen. It is just not energy efficient enough and currently also quite slow.
Sadly I think if cryptocurrencies would actually overtake physical money that goverments will create their own cryptocurrencies which are therefore not subject to the freemarket and take away control of your money. They could restirct you from buying certain things on certain sites or send your money to certain country. It would even be possible to corrupt the blockchain record.