I'm entering my third year of training to power, under the continued guidance of a coach.
we run a series of structured workouts designed to increase power output, and target each of those workouts/rides to power targets based on FTP. We also have race specific workouts designed to develop aptitude at certain activities, e.g. sprinting, bit those are adjuncts thrown in during the runup to spring crits. I don't race in earnest, so that's not something that features prominently.
the main thing is to have a regimen with a purpose, whether that's to get stronger, increase endurance, or burn calories; whatever. As mentioned above, power based training lets you monitor precisely and build a highly efficient regimen. I do most of my power training on a stationary for this reason, because it's extremely targeted and efficient.
We do road rides together in the club, but those are mainly for endurance building and deploying what was developed in the studio. Like TrojanHorse said, having power on the road has lots of uses, but I ride with power rarely, since my efforts are either maximal or not. If I have a road goal, e.g. to beat my time on a Strava segment, I push myself as much as possible and hope I was on that day, but my goals are developed in the studio, and if they're met there, the road achievements come as a matter of course.
That's not to say I wouldn't use power on the road, only that I haven't been able to get the kind of PM that works best for me. My Powertap constrains my wheel choices, which I don't like, which is why it goes out rarely, and sees most use on the trainer at home. Were money not an issue, I'd probably go SRM Campy carbon crank meter, but since it is, I'm looking more towards Garmin Vector, which also gives me multi-bike versatility.
Anyway, structured, goal based training is what makes PM usage a powerful tool, and staying on program will net results.