For "most use cases" (by far) of arbitrary fractional numbers, floats are significantly better than integer based representations, which is why they are pervasive. For certain niche uses (such as some kinds of money accounting calculations) alternative integer-based representations have some advantages, and those who need them use them where appropriate.
Disagree. IEEE floats see a disproportionate amount of use because most programming languages make them much easier to use than more appropriate representations, and people (understandably) use the representation the language guides them to rather than seriously analysing and considering the options.
