The more precisely you can count time, the more precisely and finely you can measure other things. This not only applies to fast phenomenon. It can also be used for syncing up multiple measurements made in different places; like that image of a black hole we got a couple of years ago.

It’s another step in getting a finer resolution on the universe.

Detect smaller gravity waves, possibly, hopefully.

Precision? The answer was literally in the comment you replied to.

To… get a more precise definition of a second ? It’s already pretty precise but not 100% accurate so why not ?