The length-width method of verifying the track length is admittedly imperfect. It does not meet any high standard of accuracy. What it does is to solve a problem for certain LDR races, some of which are held on tracks.
When a track is built, it is normal for a document attesting to its accuracy to be given to the track owner. Many of these documents have been lost.
So, the high school or college knows it has a 400 meter track and it knows that all the paintmarks are where they ought to be. They know it but cannot prove it to anybody. What the standards are for accuracy in high school and college athletics I don’t know.
So, the race director of an LDR run manages to obtain permission to use the track but can’t find proof that the track is what it is supposed to be. The length-width method came about to help solve the problem. Granted, a curb measurement is better, but most modern tracks don’t have permanent curbs. Rather they have sockets into which sections of curbing are installed on those days when a track meet is to be held.
I think that our solution to finding track length could be more accurate, but at a price in time and effort that might make few willing to pay.