That specific example seems more like some combination of persistence and power is required: great power suddenly and temporarily expressed could cut through stone while a weak power expressed over a long-enough time frame would have the same effect. On it's face it's only a partially true statement and thus is effectively 'BS' when presented as an aphorism.

As well, it anthropormorphizes the effect of gravity on water as 'persistence.' It might serve as a fine metaphor for human persistence but that's all.

Possibly Controversial:

I think it's key to read it a specific (overly charitable?) light.

You kind of have to take for granted that it's good advice in context. Someone is feeling discouraged and incapable facing come significant task and the best advice is to not be distracted by the feelings of incapability but rather persevere.

If you're reading it as statement on the relationship between power and persistence .. um .. you're missing it's point. Whether you agree or think it isn't well communicated is besides the point a little bit.

I think it would sound more metaphorical if you removed the indefinite articles, instead starting with "The river cuts through rock"

But that doesn't emphasise why. The point is to say "keep on truckin'".

If you have to spend a minute thinking about erosion first then it loses its punch.

> It might serve as a fine metaphor for human persistence but that's all.

That's what it's intended to do. It's not trying to be a statement about Geology.