It’s also precision. I think this is the biggest thing we’ve lost is some expression of precision.
11:45 from a digital clock is very precise. You expect something at exactly that time, and get more impatient with vagaries of traffic or delays or clocks that aren’t synched, or just that people aren’t digital
“quarter of” implies less precision. If I have to wait five minutes, you’re still not late. Regular human activity in the real world is not exact so allowing for inaccuracy is both less stressful and more practical