The problem is that HR can make it look like you are "hitting your numbers" when power would tell you that you are off.
Hear, hear!
I'm strictly a hobbyist/fred/wannabe, but a Power meter has been utterly helpful in my improvement and enjoyment.
There are some things you can do with a power meter that cannot be done with only an HRM.
After only one year of use, the best things I've learned from my power meter are:
a) to resist the tendency to clench up when putting the hammer down, and that remaining relaxed & supple during intervals enables me to continue conscious, deep, yoga-style breathing (rather than clenching up & letting my breathing just happen) lets me increase the watts dramatically toward the end of the interval, without the corresponding spike in HR.
b) higher-rpm is a great way to generate more power, BUT you must get accustomed to spinning at that higher rpm first. This might sound lame, but a power meter can teach you how to be a more efficient engine, rather than just stomping on the pedals.
When I was only using the HRM, I could jack my heart rate way up, just by spinning faster than I was accustomed, or by clenching up. But without knowing my power output in either of those situations, I was just
doing cardio without really improving.