The issues I have are twofold; heart rate lags well behind power output and heartrate can be influenced by many factors.
Looking back at my training many years ago, where I was using Joe Friel’s training bible, I was clearly overreaching by performing intervals based on heart rate. For efforts at ftp or above I was probably anaerobic for the first 30 seconds, then V02, then threshold, heart rate would catch up and then I’d probably be completing the rest of the interval below the prescribed effort level as I’d have gone too hard in the first 2 to 3 minutes. With power, inside on a smart trainer, you’re hitting the target straight away. Outside you can immediately back off or increase power. There’s no guess work, no going well above for the first few minutes and you’re completing all intervals as your coach or TR have prescribed.
On to the second issue. I go out for a ride and have heart rate and power showing. My heart rate is low compared to normal for a given power output. Why? Don’t know. Do I stop training? No, of course not. Ok, this time my heart rate is high compared to normal for a given output. Why? Do I stop training? Again, no I don’t.
If I were riding to heart rate only I’d still continue training but wouldn’t know how much power I’m putting out. So, in the first instance, riding to heart rate, I would be putting out more power than prescribed. In the second I would be putting out less. Not ideal if you’re following a training plan. It could potentially mean you aren’t working in the prescribed training zones for the workout.
Where heart rate has some use is when it’s looked at retrospectively and against power and other data ie. my heart rate was lower than normal for 4 days in a row compared to to the effort I was putting out, I haven’t had a day off for 10 days, perhaps I need some time off?
It could also be used in conjunction with power to look at decoupling. However, IMHO, heat plays a factor in this, for me anyway. If I go out and ride, I will leave in the morning, as midday approaches I could see a 10° increase which must have a bearing on heart rate. The same applies for indoor training. I keep my backdoor open and have two fans on but the room still continues to get warmer and warmer the longer the session goes on.
That’s my take on heart rate anyway. For me, a watt is a watt no matter what and therefore, power trumps heartrate.