As you've illustrated, we've come to value precision over intuition. The reason people using metric don't feel like they're missing something without organic units is because people who use the relics of those organic units don't use them in the fuzzy organic sense either anymore. When someone tells me "1 foot long" I expect exactly 12 standardized inches- not something roughly as big as my foot (even though, in my case, my foot is almost exactly 12 inches).
In modern times when we want a more organic measure we find ourselves dropping standard units (whether metric or imperial) and using random analogous items instead- like number of empire-state-buildings or 10-paces then turn left, or (more often perhaps but slightly different)- about 3 blocks away.
The moment people started caring about whether it was Henry I's nose-to-thumb length or some multiple of grains of barley dry it stopped mattering. I'm very average sized and my pace is almost exactly one yard per step (or, as you pointed out, more or less a meter as well). I would be fine using the term 'yard' in the intuitive or organic sense- but when you're using it to tell me exactly where my property line is I suddenly need precision, agreed on standards, and at that point the question of inches vs centimeters is strictly a question of familiarity (or I suppose, as the article mentions, politics).