No, you can't replace chiffres by nombres in the expression manque de chiffres.
Nous ne sommes pas en mesure [...] à cause du manque de nombres. ❌
Les fonctionnaires regrettent le manque de nombres. ❌
These sentences would make no sense. There is an infinity of nombres so there can be no lack of them.
In the other sentence, nombre would be unidiomatic.
Ces nombres minimisent la détérioration. ❓
A nombre is often the result of a dénombrement (counting) while a chiffre, in this acception, is the result of a calcul (calculation). Statistics better match the second definition.
As to why a word that means 'digit' ends up meaning 'figure', it is the usual fate of words to have their meanings evolve in the course of their lives. After all, chiffre (and 'cypher' for that matter) originally comes from a word meaning 'zero', and even actually cognates with zéro so it is simply a typical case of broadening of meanings: zero → digit → figure.