A 1 ten millionth (or whatever) fraction of the earth's circumference
surely isn't any more accurate?

Since 1983 a meter is a 1/299'792'458 of the distance light travels in
one second.
And by the way, one second is is the duration of 9'192'631'770 periods
of the radiation corresponding to the transition between the two
hyperfine levels of the ground state of the caesium-133 atom.
So it is more accurate... well, I admit you can't check it out by
yourself, you have to belive some scientist's work...