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.