Actually not a coincidence. The meter was originally defined as the length of a "seconds pendulum" (a pendulum with period two seconds). The half-period of a pendulum of length L is pi * sqrt(L/g). Set L = 1 and solve for g, and you get g = pi^2.

This doesn't work exactly because the meter eventually wasn't defined as the length of the seconds pendulum but rather as one ten-millionth of the distance from the equator to the North Pole - which turns out to be a few millimeters longer - but the idea for using something meter-sized as a unit of length came from the seconds pendulum.

...if you measure in a particular set of units. It's not so close to g = 21 mph/s, for example.

Just a coincidence. The g depends on the mass of the planet, while pi is rather universal for a perfect math circle.

In reality the g constant is not a constant, the value depends on the place of the Earth.

What are you talking about, g is roughly 7e10 furlong/fortnight^2

You must not be American. They're not that close in the USA.

g is 9.8whatever in m/s^2. If you choose inches/week^2 instead you'll get a different constant.

Many fields use geometric mass units 1 gm = G (where G is the grav constant in m/s^2) so you have g = 1 gm/s^2. Then you can drop a lot of constants for calculations.

If you make up your own units Pi^2 can be close to anything you want.