Why is Attiny85 so popular?

I didn’t mean “precise moment” literally, a couple hundred microseconds would suffice. I don’t think a comparator would be good because the analog comparison value is modified digitally (the code does a calculation), and if I wanted to output to a comparator I would need to use a DAC, so I don’t think it would save power.

Aren’t there a lot of monitoring applications where you wouldn’t want to the microcontroller to sleep because you could miss out on an event? For example, if you wanted to detect an infrared emitter/detector break beam, you wouldn’t want to have the microcontroller potentially be in sleep mode when an object quickly breaks the beam.