This is unlikely because the purpose of crypto is to make online exchanges fast, safe and anonymous. It's not a complete replacement for Fiat and especially many governments have not yet accepted the crypto as legitimate so I disagree with this view of you.
If there is some economic crisis or we see US dollar under lot of pressure, then would be a time people will be thinking of keeping their money in some trust able source and that will be time when bitcoin will became real currency and eventually replace the fiat.
Many steps must be corrected if the virtual currency will eliminate paper money because everyone understands and knows everyone until now. Banknotes can't be replaced at any time.