Sleep, caffeine, change in fitness, heat, altitude.
The only thing I find very reliable is Resting Heart Rate
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I need power in races to control pace due to adrenaline.
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I think HR is a pretty good indicator in controlled conditions, but it can be widely variable based on changing conditions and that has to be considered.
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yes, its an internal strain that under controlled conditions is showing the response to oxygen demand in muscles (at different power outputs). Seasonal variations is a big one, if its hot outside, then HR will go up because the heart has to work harder for evaporative cooling. Also if you take time off, youāll either see more responsive HR when fresh, or if you take off enough time, first a higher HR due to quick drop in cardio fitness, and then longer breaks a drop in both cardio and metabolic fitness. Or the opposite of freshness when logging a lot of hours. Things like that have to be considered when looking at HR.
Now if you take those factors into consideration, workout under generally controlled conditions, not stressed out from work/family, getting good sleep, then it should be a lot less variable. Also you know when to look at HR and when to not look at it.
So yes on bad days HR can vary widely, but so can RPE of putting out a 20 minute sweet spot interval or a long upper endurance workout.
Point being, if you have a well established rhythm in your life then during periods where fitness is steady and you are tweaking specific power durations, then HR should not vary widely. On the other hand if you took an offseason, and are in a 3-4 month base training cycle then a decrease in HR is a signal that fitness is improving (go look at people that have posted HR/lactate curves). Or pull up Intervals chart and you can see a shift in HR curve over several seasons where both cardio and metabolic fitness have increased. If you go with the HR is widely variable narrative you are missing out on a valuable tool in my opinion.
Iām sure after you finished your paragraph, the amount of caveats, IF and considerations to keep in mind to make HR useful is larger than the usefulness itself.
My youngest forgets to look at a screw head before pulling out a Philips and stripping it. HR is a tool, learn to use it or ignore it. But please donāt poop on the people that learned to use it and see obvious patterns.
Except the conditions are not controlled. I use HR as a secondary metric (together with power and RPE), but this statement is misleading. A regular schedule does not account for sleep, stress in the athleteās personal or work life, etc. Others have given more relevant factors.
HR needs a lot of context for interpretation. E. g. lower heartrate at a given power level might be a sign a increased fitness or fatigue. HR levels have been less useful in my experience. I use HR to pace outdoor endurance rides, because I find that easier than power.
guess Iām a freak of nature 
I have always felt these caveats apply to power as well. Altitude, heat, stress, etc. I would be surprised if a regular user of TR sees much HR variation and if they do they are probably changing intensity.
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absolutely
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No. Power is power. Whether and how well you can manage a workout depends on the same aforementioned factors. Only altitude is different, because that does reduce the amount of O2 you breathe in, and does shift your power zones downward.
Even the order of workouts can cause a shift of 8-10 bpm: if I tack on an endurance workout after a hard workout, my heart rate is usually in the high 130s or low 140s as opposed to 120ā135 bpm range. Should I lower my power targets to hit HR targets? I donāt.
HR has its place in training, but it is a secondary metric.
I was only responding to your claim that this was ācontrolledā.
That makes HR primary 
That sounds like an attempt to make a gotcha argument than to engage in discussion.
During my last two races (a crit race and a short hill climb TT), my heart rate was useless, it quickly increased to >175 bpm and stayed at essentially HR max for the last few minutes (182ā184 bpm). All HR told me was that yup, I canāt go any faster. Power was much more important in both for me.
HR is the least important for me, power and RPE is where I focus on.
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That makes two of us.
My heart rate is incredibly predictable pretty much every day. Not only is my heart rate predictable, I also pretty much know when my hr is NOT going to be ānormalā from life stress, adrenaline, lack of sleep, anxiety, too much caffeine, too many IPAs the night before, travel, etc, All variables that are trivial to take into account.
Other athletes may not understand how to account for their own variability, but thatās on them.
Ultimately Iām controlling by RPE, and hr and power typically fall within an expected range for any given RPE and when hr and power isnāt within the expected range, I can pretty accurately guess why.
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Three of us, along with Ryan above.
Yup. Iāll also throw ātime for a new strapā and ādonāt know but Iāll keep an eye out for a patternā as things that happen every couple years.
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Power is king. In my view, HR is about triangulation, and a signal of changes in metabolic fitness. Great tool for those times Iām on a (indoor or rented outdoor) bike without power.
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Yeah, power then feel. I often struggle with RPE so HR is usually better at keeping me honest. Sometimes my head is so wrapped up in work drama I have to extend my warmup before doing the work.
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