There have been many examples of badly designed floating-point numbers, e.g. those used by the IBM mainframes and those used by the DEC minicomputers. In both cases, minimizing the costs for computer vendors was prioritized over the properties needed by the end users.
In scientific and technical computations, a constant relative error over the entire range of the numbers is optimal.
Only logarithms would be better than IEEE floats, but the addition and subtraction of numbers stored as logarithms is too slow, so the IEEE floating-point numbers are a compromise between the speed of multiplication and the speed of addition.
Posits redistribute the relative error over the range of numbers, increasing the precision of numbers close to unity by reducing the precision of numbers far from unity. This is a property that may seem desirable for input data and output data, but it is extremely undesirable for the intermediate values that are generated in computations.
Even for input data and output data, in engineering there are many characteristic values of parts used in manufacturing, such as electronic components, where constant relative errors are needed over a range greater than 10^9 or even greater than 10^12 (e.g. the values of standard resistors, with a given tolerance, may vary from milliohms to gigaohms and those of standard capacitors from femtofarads to farads; it would not be acceptable to represent such nominal values as posits, with a tolerance depending on the nominal value).
There may exist some applications where this is useful, but all such applications are among those that need low precision numbers, of 32 bits or less. So 16-bit or even 32-bit posits might be useful in certain circumstances, but it is pretty certain that 64-bit or bigger posits will always be inferior to IEEE floating-point numbers.
The problem is that while the IEEE floating-point numbers are either optimal or at least acceptable in almost all applications, the fact that posits might be better only in certain special applications makes unlikely that the development of dedicated fast hardware for them can be worthwhile.
Even if some applications might indeed like a better precision for numbers close to unity, for those applications posits must contend not only with floating-point numbers but also with fixed-point numbers, which do not need any special hardware and they can be implemented in any standard CPU with a simple software library.
Fixed-point numbers have even better precision than posits for numbers close to unity, but posits have a greater range, where their precision drops quickly towards the extremities of the range.
So the application domain of posits is squeezed between those of floating-point numbers and those of fixed-point numbers, leaving a very small number of applications where posits are optimal.
I am not aware of any application that would justify the additional cost for posit-processing hardware. I think that the only chance for posits would be if someone would show that some posit format is better for certain ML/AI/LLM computations than narrow FP formats like BF16, FP8, FP4.
That will be the only use case that could find people willing to pay enough money for the design of posit-processing hardware, in some kind of NPU for training or for inference.
Like I have said, for technical/scientific computing posits are much inferior to FP64, graphic applications are happy with FP32 and FP16 and they do not have any reason for a change, while the applications that need high precision around unity are happy with fixed-point numbers and they also do not have any incentive to change.