I can relate to that sense of obligation. For me, it's also about establishing a routine and sticking to it. Once I'm out the door, I usually find my motivation in the fresh air and quiet morning streets.
I'm not elite, but I've dabbled in HR training. For me, it's been helpful for pacing and recovery, but I don't obsess over the numbers. I think it's a tool, not a rule. I use it to gauge my effort, but I also listen to my body. If you're finding it's a distraction, maybe try using it as a guideline rather than a hard and fast rule. It's supposed to support your training, not dictate it.