> ... but some things have an impact on people's quality of life: nutrition, healthcare, and psychological well-being.

I would perhaps classify that as "immediate" impact, not "lack of impact".

Number theory has driven computer science, calculus, statistics, and so on.

CS, calculus, stats... they all drive (for example) "nutrition". For example, how do you know what a "vitamin" is? How do you measure it? How do you quantify it's effects on the body (and mind)? A whackload of analysis DEPENDS on number theory for us to understand almost everything about the natural world!