That really overstates the issue. Whole domains of finance run just fine on doubles.
If you're doing Monte Carlo options pricing over interest rate paths, and you're interested in the risk metrics, like durations, convexity, vega, and so on, no one cares what your rounding convention is. doubles are just fine, thank you. How are you going to force `exp(-rt)cashflow` to be an integer? Or the normal CDF?
Yes, there are domains where ints make sense. But it's certainly not universal, you just need to make the right engineering choice.