Basically the model you're using implies that if two people are equal over 10k and 800m, they would be the same over 3k. Mathematically that may seem convenient, but I think there are other factors that come into play.
To give an extreme example, if you take two guys who could run a 2:20 marathon and one could run 13:50 and the other could run 14:10 for a 5k, I don't think it's necessarily the case that the 13:50 guy would take the 14:10 guy in a 40. Different factors (VO2 max, anaerobic threshold, raw leg speed, ability to handle fatigue on legs) carry different relative weights in different events, and the precise mix is very likely not the exact same for all people.