Several years ago when I discovered some of the historical work on interval arithmetic, I was astounded to find that there was a notable contingent in the 60s that was urging hardware developers to make interval arithmetic be the basic design of new CPUs, and saying quite forcefully that if we simply went with "normal" integers and floating point, we'd be unable to correctly model the world.
I think as another commenter pointed out, interval arithmetic’s problem is that while it acknowledges the reality of uncertainty, its model of uncertainty is so simplistic, in many applications it is unusable. So making it the standard primitive, could potentially result in the situation where apps that don’t need to explicitly model uncertainty at all have to pay the price of being forced to do so; meanwhile, apps which need a more realistic model of uncertainty are being forced to do so while being hamstrung by its interactions with another overly simple model. It is one of those ideas which sounds great in theory, but there are good reasons it never succeeded in practice-the space of use cases where explicitly modelling uncertainty is desirable, but where the simplistic model of interval arithmetic is entirely adequate, is rather small-a standard primitive which only addresses the needs of a narrow subset of use cases is not a good architecture