Three 3-shot groups provide 9 data points collected under conditions similar to how the rifle might be used in the field. I could care less what the cone of fire will be after three shots. For a target or varmint rifle 10 shots make perfect sense.
At the risk of repeating myself - let a random number generator pick 3 numbers between 1 and 100. How often do you think it will pick both 1 and 100? Pretty much never, obviously. Now have the random number generator pick 30 numbers, and while it likely won't pick both 1 and 100, it will likely get at least one down into the 10s and one up until the 90s.
Now, imagine you did not know in advance the range was 1 and 100, and the purpose of your test was to figure out the maximum possible spread. Now amplify that principle by visualizing random points in a circle of unknown size, instead of just numbers in a linear range. That's how measuring accuracy works. Half the time, your groups will be half the size of what the gun might actually shoot.
To be clear, I don't shoot 30 shot groups every time I go to the range, nor do I need to, nor do I suggest you do. In the life of any given gun, I'll do it once for any given load I intend to shoot a lot of, which for most of my guns is maybe 2 or 3. Once I know what the gun is capable of, I shoot 3 or 5 shot groups like everyone else (and often just 1 or 2 shots when simply checking zero), and as long as they print inside the cone I know the gun can shoot into, that's all I need to know.