" HR measures what you are producing and PM measures what comes out" What?
OK what I meant was your HR is a measure of the stress your body is under. It is a response to the demand placed upon it. It is a lagging indicator. So here are some of the effects I have observed.
You can't max your heart rate in a short burst, say 30 seconds.
Heat creates stress for your body and this will be reflected in your heart rate.
If you are ill or over training your heart rate may be higher than expected or not willing to come up to expected levels.
You can't get to your max working heart rate on a bike unless you lift the cadence to get the response you need.
Heart rate rises as you train - thermal drift, acidosis etc.
So it is an indicator of how your body is doing.
Power is a measure of what you are delivering on the outside of your body, either through the pedal or back wheel and does not measure anything in terms of how it was delivered, ie what comes out, not how it got there.
So your HR is a physiological indicator and the power measure is a mechanical measure and each has it's place.
The two come in to play as a measure of efficiency and fitness. If you train at a fixed power, over time you would expect your HR to come down as you adapt, it will stop coming down when the adaptation is complete. So continuing to train at this level will maintain fitness but not improve it. So you are better to introduce a change of some kind and possibly come back and restest at that level.
If you try to increase the load because a power programme says so, you can find that you are in difficulty because you have not trained sufficiently at a lower power because you have not completed adaptation. You can increase the load too fast or waste time by not increasing it enough. Your HR can indicate that adaptation is complete.
You can use your HR as a measure of how efficient you are at delivering power. You have to be careful here in that a low cadence/big gear will reduce your HR and a higher cadence/low gear increase it for a given power output. So extremes can be misleading.
HTH