Why is Attiny85 so popular?

It is impossible to know the “precise moment” that something occurs. An ADC reading can take a couple of hundred microseconds.

A comparator can compare an input to another voltage, set by a standard or digital potentiometer, and is thus adjustable by the end user. Furthermore, the comparator has higher resolution than the ADC and can wake the part up from sleep. So the ADC is neither necessary nor desired.

Geeze, of course "precise moment" is all relative.

Measuring range with optical LIDAR for topographic mapping needs fractional-nanosecond precision.

Measuring speed bumps in a road traveled, somewhat less.

Measuring radio signal round trip to Pluto takes many hours.

ADCs can be about as fast as you have money for! One microsecond ADC time for 10-12 bits is built into ARM MCUs that cost $6.