I think the specific value that stated in the NEC is less important than the fact that a value, some value, any value, is stated. If an inspector cannot use some type of measurement to verify compliance, then the rule has no meaning. There really is no substantial difference in risk between a tap that is 10 feet long and one that is 11 feet long. But there is a substantial difference in risk between a tap that is 10 feet long and one that is 100 feet long. I believe that a line must be drawn, but I cannot tell you why the line was drawn specifically at 10 feet.
Please keep in mind the reason for setting a limit. The primary rule is that we must protect conductors from overcurrent, and we must install that protection at the location at which the conductor receives its energy. The "Tap Rules" allow us to digress from that primary rule. We are allowing the protection to take place some distance from the point at which the conductor receives its energy. If a fault takes place upstream of the protective component (i.e., the fuse or breaker), then the conductor will not be protected. We can accept that risk, so long as the conductors are protected against physical damage, and so long as the protective device is not too far away from the energy source. That is why the 10 foot limit was established. Someone else will have to chime in on why the limit was set at 10 feet.