fermi approximations happen all the time in astronomy. The numbers are frequently so large that the only meaningful quality is how many orders of magnitude it has.

More to the point, using pi makes calculating things much harder. For example, we don’t really need a precise distance for most things; so using “3” makes the calculation unnecessarily spend time in computation.

It’s like the old joke, “what’s the difference between a millionaire and a billionaire?” (“About a billion.”)