Some environments only expose float as the number type, love2d being one I know. Fortunately love is built on LuaJIT, which does support integer math through the built-in ‘ffi’ library.

My multiplayer arena game rounds reasonably-sized floats and compares them in the presentation layer, but uses fixed point integer math in the core rollback simulation

(I believe JS is a similar story, its number can be either int or float with no way to guarantee integer-only math. I never needed to consider the difference outside of currency for webdev, so I’m less sure)

I need it all the time. A very common case is caching of (expensive) computations. Let's say you have a parameter for an audio plugin and every parameter change requires some non-trivial and possibly expensive computation (e.g. calculation of filter coefficients). To avoid wasting CPU cycles on every audio sample, you only do the (re)calculation when the parameter has actually changed:

  double freq = getInput(0);
  if (freq != mLastFreq) {
    calculateCoefficients(freq);
    mLastFreq = freq;
  }

Also, keep in mind that certain languages, such as JS, store all numbers as double-precision floating point numbers. So every time you are writing a numeric for-loop in JS you are implicitly relying on floating point equality :)