Also, I wanted to add that when considering Strava live segments people mostly think about very short sprint like segments. But I think the real value in medium to long segments that are complete logical routes, for example an entire push from a trailhead to a mountain summit or an entire popular route such as an FKT route - see https://fastestknowntime.com/.
This is where live segments have a lot of value. Using a segment becomes more like a virtual race where you try to improve your previous result or chase the record, or perhaps even chase a person ahead of you on the leaderboard. By the way, Coros allows to choose which time you want to compete against - see https://support.coros.com/hc/en-us/articles/32280188180372-Using-Strava-Live-Segments-on-COROS-Watches