You should be fine with leaving fiat on exchanges because exchanges getting hacked is mostly concerned with stolen bitcoin and cryptocurrencies and not fiat; Assuming you're actually referring to real fiat money and not stablecoins.
Hackers and their fund movements with fiat (real fiat) will be traced more easily when they make movements with crypto and some mixing combination methods to launder their hacked crypto. The point is there is no guarantee that after hackers were caught, all victims will get their funds back.
Nothing is 100% safe: from exchanges to fiats, stable coins so the best approach is decentralize your funds in some sort of money storage: fiat + stable coins.
I know for crypto enthusiasts, stable coins are their more favorite as convenience they bring to users. With their fast transaction speeds and wide adoption on exchanges, people can move stable coins around and buy up dips. With fiat, the adoption is less and people usually have to bear a temp loss in rate to buy Bitcoin with fiat or to convert fiat to stablecoin then buy bitcoin with stable coin. It is true when market is in hot mood.
DAI is a good stable coin due to its decentralization. USDT is more used but beware of risks and related drama, potential lawsuit on USDT. I'd like to decentralize my stablecoin allocation into a few stable coins and in different wallets.
PSA: Most Stablecoins Can Be Frozen, Even in Your Own Wallets