these don't hold for floats even though most math formulas and compiler optimizations rely on these to hold.

Most compilers have an option like -fassociative-math that explicitly allows optimization under the assumption of associativity and distributivity.

Real programmers use fixed point representation and make sure the bounds don't overflow/underflow unexpectedly.

So you complain that floating-point is bad because it's not associative but then suggest that we use fixed-point instead (which is also nonassociative), but it's okay, because it's fine as long as you do thing that programmers rarely do.

Let's ban all hardware floating-point implementation : Just imagine future alien archeologists having a laugh at us when they look at our chips and think "no wonder they were doomed they can't even do a+b right : its foundations were built on sand".

Ah, you're the kind of person who sees that 0.1 + 0.2 != 0.3 and decides to go on a crusade against floating-point because of it. By the way, fixed point has that exact same bug: it's a fault that is caused by the base being different more than the other principles of the floating-point type.

Floating-point has trade-offs; a good programmer understands the trade-offs of floating-point and will not ask more of it than it can provide.