Please stop repeating this nonsense. It's purely based on ignorance and only pushes more people into it.
This is universally repeated by people that have not written any modern financial software and who don't understand floats.
If all you do is add US dollars and pennies, then maybe you can get by with integers. Once you do anything else in modern finance integers puke completely. There's a reason scientific computing doesn't use integers, but prefers floats/double - they are much easier to use to get the best answers per compute.
For example, if you need to do anything with interest, which is fundamental, you'll soon find doubles are vastly better than bitsize equivalent integers, no matter what scaling/fixed-point/other tricks you employ. Add in currency differences (Yen to USD is a large multiplier, etc), any longer range calculations (50-100 year loans or flows), aggregation of varying items, derivatives, and on and on. Telling anyone in the field you're going to use integers will get you laughed at - the problem is not floats, the problem is the programmer hasn't taken a single class on numerical analysis and has not enough skill to do financial software.
For example, one of the simplest things one needs to do is compute compound interest, say computing mortgage tables, with say principal P (left), annual (or weekly, or daily..) rate R, for N years, periodic payment m, and you want to compute payments and schedule.
In reals, this is simple: each cycle you do something like
r = (1+R/12)
P -= m
P = (1+r)*P
Then you write out values you need.
Trying to write this software with integers, no matter what scaling, fixed-point, shifting, and other tricks you employ, is going to be vastly more complex and error prone than simply using doubles. If you don't think so, pick a bit budget, say 32, or 64, for you base number type, and show me your code. Then I'll show you the naive one with doubles vastly outperforms your code.
This continues through all of modern finance.
So stop repeating this ignorance that one should use integers for money - that is purely a result of being ignorant about how to write robust numerical code, and only pushes people down a far worse rabbit hole when they hit issues with ints and try to patch them one at a time via ad-hoc hacks.
There's a reason scientists use floating point, not ints, to do real numerical work.