Despite these examples, it can be argued that underflow rarely matters, and so, why bother? However, this argument turns upon itself.
In the absence of gradual underflow, user programs need to be sensitive to the implicit in accuracy threshold. For example, in single precision, if underflow occurs in some parts of a calculation, and abrupt underflow is used to replace underflowed results with 0, then accuracy can be guaranteed only to around 10-31, not 10-38, the usual lower range for single-precision exponents.
This means that programmers need to implement their own method of detecting when they are approaching this inaccuracy threshold, or else abandon the quest for a robust, stable implementation of their algorithm.
Some algorithms can be scaled so that computations don't take place in the constricted area near zero. However, scaling the algorithm and detecting the inaccuracy threshold can be difficult and time-consuming, even if it is not necessary for most data.