I think you might be confusing "measure" with "observe". Measure in this discussion has a distinct quantitative implication.

You've never had one steak you prefer to another without doing quantitative analysis on it?

I love making cocktails and I can definitely tell better from worse, noting qualitative differences (a bit dry, too sweet, mouthfeel a bit thick) with absolutely no quantitative measurements involved.

I can certainly tell the difference between a good and bad violinist without measuring anything.

From a different perspective: many of my favorite movies have a 3.5 star rating on Amazon, in this case the measure does not correlate well with my sense of improvement.

Try a blind test for your cocktails (you could follow https://en.wikipedia.org/wiki/Lady_tasting_tea ). The results may surprise you.

Surely burning witches to improve the weather is exactly an example of metric use gone awry? To your point though, it is exceedingly common to know we are better at something without a clear metric. It is not controversial to suggest that someone may be better now at communicating than they were as a child, even though there is no clear way to define this.