rivers

The principle is that bends in rivers tend to grow as erosion happens on the outside of the bend and soil deposition on the inside.

The average of an empty set is undefined, and oofabz's objection above pertains: rivers almost surely lack lengths.

Hydro is likely going in reverse as many rivers were returned to original condition for environmental reasons.

While it would technically apply to rivers as well, the website seems to be using a single significant digit.

However, what they mean when they say this is this more precise fact: if there were an infinite number of rivers formed like those on Earth, the average sinuosity of that infinite collection of rivers would be exactly π.

Why on earth would the rivers of the world have an average sinuosity of pi?

The right answer may not be pi, but the data shown make a compelling case that rivers do tend to some average value.

As a sidenote, there are active human efforts to keep certain rivers, like the Mississippi, from meandering too far from their current locations.

I entered a few rivers by just copying data out of the Wikipedia side bars for them.

The complexities there don't seem to have a correlary to the rivers.

On the other hand, rivers' bends are constantly amplified by erosion.

Yes, boundaries often coincide with rivers and mountain ridges.

Rivers are super dynamic and are effectively a side effect of localized water cycles and geology.

Rivers and mountains are topography and geology material.

Rivers have a finite width, so once the distance between your measurements is smaller than the width of the river, the measured length will converge to the true length.