Interval arithmetic isn't useful because it only tells you the extreme values, but not how likely these values are. So you have to interpret them as uniform random. Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more. Therefore interval arithmetic basically has an undefined underlying distribution that can change easily without being tracked.

> Operations like multiplications change the shape of these distributions, so then uniform random isn't applicable any more.

Doesn't addition as well? Like if you roll d6+d6, the output range is 2-12, but it's not nearly the same as if you rolled d11+1.