You still can't divide by zero, it just doesn't result in an error state that stops execution. The inf and NaN values are sentinel values that you still have to check for after the calculation to know if it went awry.
Operations on those sentinel values are also defined. This can affect when checking needs to be done in optimized code.
Personally, I am lazy, so I don’t check the mxcsr register before I start running my programs. Maybe gcc does something by default, I don’t know. IMO legitimate division by zero is rare but not impossible, so if you do it, the onus is on you to make sure the flags are set up right.
It's well-defined is all that really matters AFAIC.
I'll give two examples from a recent project where I very intentionally divided by zero. First one was about solving a zero in a derivative and check if it falls on 0..1 range. This exploits the fact that (x < NaN) is always false and comparisons with +/- inf behave as expected.
float t = a / b; // might divide by zero. NaN if a and b == 0.0, +/- inf if b == 0.0
if (t > 0.0 && t < 1.0) {
// we don't get here if t is +/- inf or nan
split_at(t); // do the thing
}
f32x8 x = a / b; // might divide by zero
return simd_min(simd_max(0.0, x), 1.0); // returns 0 for -inf or nan, 1 for +inf