What is "properly" though? There's many real numbers that don't have finite representation. Arbitrary precision is all well and good, but as long as you're expressing things as binary-mantissa-times-2^x, you aren't going to be able to precisely represent 0.3. You could respond by saying that languages should only have rationals, not reals, but then you lose the ability to apply transcendental functions to your numbers, or to use irrational numbers like pi or e.
Performance is only part of the problem, and what it prevents is more-precise floats (or unums or decimal floats or whatever). The other part of the problem is that we want computers with a finite amount of memory to represent numbers that are mathematically impossible to fit in that memory, so we have to work with approximations. IEEE-754 is a really fast approximator that does a good job of covering the reals with integers at magnitudes that people tend to use, so it's longevity makes sense to me.
Performance is only part of the problem, and what it prevents is more-precise floats (or unums or decimal floats or whatever). The other part of the problem is that we want computers with a finite amount of memory to represent numbers that are mathematically impossible to fit in that memory, so we have to work with approximations. IEEE-754 is a really fast approximator that does a good job of covering the reals with integers at magnitudes that people tend to use, so it's longevity makes sense to me.