dnd 5th – Is the rarity of objects really related to its power?

Answers to questions such as What should be the rarity index for this homebrew healing brick? are usually based on the comparison of the effects of an article. On the other hand, there are questions like

it makes me doubt whether scarcity is really, really based on power.

Is there a rule that the most powerful objects should be rarer? Or is it possible to have, for example, an artifact that shines only in the presence of an elven baby because it is a tear-mother-goddess of the elven pantheon, and that its rarity has nothing to do with a non-existent power?

The tear was only one example. I am looking for a general rule or a guideline, or its absence.