The numbers simply do not bear illustrate the superiority of an all-volunteer force.

During the Civil War, the Union had a approximate strength of 2 million men, with 168,000 drafted, for a percentage of about 8.5%. With battlefield losses of about 20%, an 8.5% reduction in force would have been quite significant.

In WW1, the US had a personnel strength of about 4.7 million. Of that, about 3 million were inductees. That's about 64% of the total force strength.

During WW2, the US had about 13 million men under arms, with 11 million inductees; conscripts constituting about 85% of the force.

Now, the US has been involved in the so-called era of persistent conflict for eleven years, with more to come. According to the Joint Chiefs Chairman:

But in any case, I believe I’m chairman at a time that seems less dangerous but it’s actually more dangerous. That’s the essence of what I describe as a security paradox. Although geopolitical trends are ushering in greater levels of peace and stability worldwide, destructive technologies are available to a wider and more disparate pool of adversaries. Highly accurate ballistic missiles are prevalent in every theater. Bombs made out of fertilizer can defeat and destroy our toughest mine-resistant vehicles. A cyberattack could stop this society in its tracks. And these are real threats that we face today.

What truly concerns me as chairman is that these lethal and destructive technologies are proliferating in two directions. They’re proliferating horizontally across advanced militaries in the world, and they’re proliferating vertically, down to nonstate actors, especially insurgents, terrorist groups and even transnational organized crime. As a result, more people have the ability to harm us or deny us the ability to act than at any point in my life. And that’s the security paradox.
Today, the US has an active duty force of about 1 million men, none of which are conscripts. Yet the total expenditure for the GWoT has exceeded that of every other US conflict (yes, including WW2). In the Civil War, WW1, WW2, Korea, and Vietnam, there were definitive outcomes: 3 favorable, 1 arguable, and one negative. That's not a bad track record.

During the most recent draft era (1940 - 1973), the US entered the following "wars of choice": Korea, Vietnam, and Dominican Republic. Since 1973, the US pursued the following "wars of choice": Grenada, Panama, Colombia, Iraq I and II, Bosnia/Serbia/etc, Haiti, and Libya. One could arguably add Yemen, Djibouti, Philippines, and Somalia depending on definitions. Of those, only Grenada, Panama, Bosnia, and Iraq I had a definitive and favorable outcome.

So, the institutional momentum is increasing towards a greater number of military operations accompanied by higher costs (the causes of which are well documented by Pentagon watchers) and lesser definite and favorable outcomes. Even with the economic challenges faced by the country, there is little indication of slowing, much less reversal. Higher and more complex demands are being placed on a smaller, more expensive force, with the predictable results of poor conflict outcomes, higher personnel attrition, and high service crime rates. A military "elite" (mentioned earlier in this thread) has it good with higher pay, etc than their past counterparts. But that doesn't indicate whatsoever that the total force is doing any better (i.e. winning more wars more effectively; which on the whole it isn't); it only means that living conditions expectations have increased.

Ken, and the general consensus it seems, assigns this problem to outdated personnel and training systems, and various Congressional policies; though, at the same time, it is pointed out that Congress has also dramatically increased the amount of money spent on the services, with a significant portion invested in training, personnel, and acquisition. Since 1973 (the end of the most recent draft era), Congress has elected to declare war a total of zero times, has issued a military force authorization a grand three times, and has had its war powers ignored by the President at least four times. And even though Congress has required that every federal department comply with standard financial practices, the Defense Department is the only one that has failed to do so. That doesn't incite much confidence in Congress' ability (or willingness?) to influence military policy, with specific regards to engaging in and favorably terminating conflict.

So where is, according to Ken, the "world historical record" that demonstrates the "superiority" of the all-volunteer force? Every major US conflict was won with a substantial number of conscripts. The US was engaged in less conflict (and at less cost per conflict!) with conscription than without. And, lastly, the powers of Congress were substantially stronger relative to the President in regards to war-making in the most recent draft era than with today's all-volunteer force.