The takes I've seen from pretty much all the numerical analysts is that posits are not really viable as a replacement for floating-point; they're just a much worse implementation. There are a lot of flaws with IEEE 754 (I'm upset that NaN != NaN, e.g., and sNaNs seem to be universally considered a design mistake), but the underlying theory behind it is very well worked-out, and even its more controversial features (like denormals) turn out to have been vital innovations.

One of the issues with posits from a numerical perspective is that it's main claim to fame of being more accurate is handled by having the number of precision bits being dependent on the exponent value, which means it's a return to the days of having to scale your input so that the values are around unity to maximize, rather than the promise of floating-point of being scale-independent.