the post race analysis of the power data is definitely useful. for example, you might find that in races your short efforts as you close gaps are a bit higher than in training (eg 30-40s, 1 min, peaks), while the rest of the curve isn't. this may be especially the case at the beginning of the season. If that's the case you might want to try and work towards improving those peaks in training. Even w/o a coach, analyzing the numbers can also be good for your motivation to get better racing results. you might find that you got a good race result and still operated well within your power curve. that is a clear signal that you can place higher still, if you get your strategy right. All this said, I would not really look at my power when actually racing unless I am in a breakaway, or if I feel good and want to confirm that I am pushing solid numbers on a climb (to motivate myself).
That said, some riders like to race entirely on feel, which is fair enough, and I have done that plenty of times. But I don't really think there is anything to lose by analyzing the numbers after the race. If they are really crap and you sucked, you can always delete the file : -) and move on! or, even better, use it as a reminder that you need to do better than that!