Crypto currencies are not a big threat now for the fiat currencies because only very less people who knows about cryptos and even them uses crypto as an asset not an currency so if that continues forever there is no big threat for the fiat currencies because we need fiat to cashout the cryptos.But when the people starts to use crypto as direct payment surely it will replace the fiat in big part but not completely.
As time goes on, more people will use crypto, so crypto will become a threat gradually.