Really, I don't see anything good in saving fiat money now. I rather save some of BTC or ETH or some altcoins. Fiat money is a passed stage for me 
Saving fiat money is a good idea after all it is not like fiat is going to disappear tomorrow or anything, if you are not sure in what to invest then saving in fiat is a good idea until you take your decision, now if you already know in what you want to invest then it is the moment to take action and do it especially if you want to invest in cryptocurrencies since the current prices will not last forever.