It's a very rough rule of thumb, take these numbers with a grain of salt. It could very well be that some food activates in 5 minutes etc. Different insulin types also have different curves.

Anyways there are studies about the "inject 15min before food" approach: eg. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2945151/

You forget one very important rule: it's all vibes :D No but seriously: insulin starts to act after 20mins. Its action is more like a flat parabola.

Glucose acts more in harsh peaks. So you want the glucose peak to hit when you are at the maximum of insulin action. Hence the 15mins delay.

This is all roughly speaking, YMMV.