That depends on how easy it is to get out if it.

If the influential always go to the coast guard or whatever, war is less meaningful for those in power.

“That depends on how easy it is to get out if it.”

Exactly. That’s why I despise ppl whose connections got them out of the draft. For everyone of those punks, another one of McNamara's morons had to be drafted.

Mohamad Ali, on the other hand, he had the courage to go to jail.

Burn your draft card, escape to Canada, or simply refuse. But those who use university exemptions or bone spurs can go to hell.

Escaping to Canada increases the amount of McNamara's morons needed the same as a university exemption or bone spurs does.

The only difference between your methods is consequences for the person undertaking it, not those that have to replace them. You appear to want people avoiding being drafted to suffer. Pretty odd if you otherwise sympathise with them.

Even though Ali had the courage to go to jail, by your reasoning in the previous paragraph, someone else “had to” be drafted in his place.

Perhaps you won’t go so far as to call conscription kidnapping, but you seem to sympathize at least a bit with people having scruples over being shipped off involuntarily to wage aggressive war. Now, you may admit that some are principled objectors, and others may simply believe that dirty work is beneath them. The more important question is whether the draft is just. If so, then any refusal by the able is wrong, and if not, we may not condemn resistance in any peaceful form.

The reality of deferments for the politically connected and most especially those for the children and grandchildren of politicians who vote for war makes utter propaganda the notion that disinterested philosopher-kings or a technocratic elite are merely acting to promote the greatest good for the greatest number.

Does this argument back-test successfully?

Has the US suffered fewer war-fatalities in the era(s) where it had a draft (including the Civil War, WW1, WW2, & Vietnam), or in the era where it has an all-volunteer force (since 1973)?

That’s almost impossible to compare due to advances in both weapons and protective equipment.

And yet, we have to try to make such comparisons to make such sweeping judgements as "a draft makes war less likely".

The quality of weapons and armor (and training and medical care!) also isn't independent of the draft/volunteer dimension. A all-volunteer-force may find it necessary to invest more in each, because fewer people will volunteer to be part of a military force that tries to win with raw & disposable strength-of-numbers.

So maybe the all-volunteer-force "raises the cost of war" even more, considering financial costs & second-order effects, and thus best deters war? It's possible, which is why such claims need to be evaluated against history, not just asserted.

Probably not but a lot has changed.