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.