Yes, I have. I also have a math PhD, have written scads of scientific and numerical software, and have written articles on floating-point math. So now that we have enough of our personal accolades out of the way, let's focus on facts regarding calculations:
How did you use ints to compute compounded interest on loans? I asked that above, and you avoided it. I ask again.
For example, suppose you have a mortgage where you lent $100K at 5% annual, compounded 12 times a year, for 30 years, and you need basic values regarding this loan.
Often in such calculations you need to compute 100K*(1+0.05/12)^360. How do you do that with integers? Naively you need (1+(1/20)/12)^360, which as a reduced fraction each of the numerator and denominator have over 2800 binary digits. Do you really do this with integers?
Now put that in a mortgage trading or pricing system where it needs to do millions/billions of those per second.
Doing this as double gives enough precision to make the difference between computed and infinitely precise negligible (approx. 10^-17 error).
It's easy to make examples where doing incremental calculations, rounding to pennies and storing, results in long term error. In these cases I don't see how do to it with integers without massive overhead.
And this is a trivial, common example. Doing stuff like hedge fund stuff, or anything using numerical integration to make models for pricing, would be astounding hardly to do with integer only math.
What finance software did you write? A simple ledger works fine as integers. Anything more complex will hit performance and scaling issues soon after the basics.