Some people simply will not undertake an activity they wish to improve upon (exercise, coding, playing an instrument etc) without objective numbers guiding them and relaying their progress.
Others, like myself and perhaps OP, are happy enough to undertake an activity and be less scientific about their performance so long as they "feel" they are making progress and more importantly enjoy the activity.
To add to my previous post. I do try to strike a balance. For example the vast majority of the time I don't measure myself, but every now and then for curiosity I'll strap on a heart rate monitor and mobile app like MayMyRun to see how I'm performing versus a few months ago. I still don't have the voice shouting progress in my headphones, and I still run without music, but it's interesting to see the results and a nice outcome if they have improved.
This and it also depends on your experience. When I started running I also used a heart rate monitor and training plans guided by an app. By the time I got a feeling how fast I can run I ditched the heart rate strap. Now I still use a running watch with gps, but do not let it set my pace. On the other hand, I'm not ino competitive running, I'm doing it just for fun.
For me, heart rate monitors and Strava have greatly improved my running and cycling enjoyment, as well as made me more likely to run. Strava has lots of metrics, and encourages competition with others, and my heart rate monitor (and accompanying watch that tells me my heart rate) gives me direct feedback to how hard I am running, and if I need to slow down or pick up the pace.
I too went all in on the numbers, heart rate monitor, detailed running plans, 5k competitive park runs every weekend. I thought I should run at least x times a week or I'm doing it wrong.
Holy cow, did it suck the enjoyment out of it. Having MapMyRun shout in my ear every kilometer meant I couldn't just zone out and enjoy the run.
Then I fell down some stairs at a tube station in London and popped my patella. Fortunately it popped straight back in, and it healed on its own but it took months and it was over winter so I stopped running.
When I got back in to it I decided it was time to go "au naturel". No head phones, no shouty applications, just me and the road. I've kept it up, and don't ever plan to go back to my former approach. I've also found that if I switch up cycling and running there's less strain on my healed knee whilst still allowing me to exercise 2 - 3 times a week. I always recommend to people now that if they can they should cycle and run.