Small nit, but floats aren't inaccurate, they have non uniform precision. Some float operations can be inaccurate, but that's rather path dependent...
One problem with -ffast-math is that a) it sounds appealing and b) people don't understand floats, so lots of people turn it on without understanding what it does, and that can introduce subtle problems in code they didn't write.
Sometimes in computational code it makes sense e.g. to get rid of denorms, but a very small fraction of programmers understand this properly, or ever will.
I wish they had named it something scary sounding.
"Some times" here being almost all the time. It is rare that your code will break without denormals if it doesn't already have precision problems with them.