I find I go a lot faster when I ride my bike that has a power meter on it, compared to the one that doesn’t. I put his down to having a number in front of me that drops to zero *the second* I free wheel down a hill or take a breather. There is no hiding – unlike with say a heart rate monitor which will still be high even if I’ve slackened it off.
I also find it useful for gauging effort – I know if I’m putting down 350w I can do it for a certain amount of time – useful when trying for Strava PRs. Also helpful for pacing when doing long sportives – as long as I keep the power below 230 ish I can go pretty much indefinitely, and if I’m below 170 I need to start trying again.
Can’t say I really do structured training on it, but all of the above I find very useful. Tho I wouldn’t bother with one on an MTB. I may well get a second one for the commuter at some point.