Are We Sure the Draft's Constitutional?

During the Civil War, the Union government instituted a draft to supplement the ranks of the army as the war took its toll over the first couple of years. Many Northerners didn't much like this. In fact, much Northern rhetoric against the draft compared it to slavery, and you can see why: slavery and conscription are both, very literally speaking, forms of involuntary servitude. I think this fact, that many Northerners thought a draft akin to slavery, interesting in light of the World War One-era Supreme Court case rejecting a claim that the draft was unconstitutional. Only in one paragraph near the very end of the opinion does the Court even consider the Thirteenth Amendment claim, i.e. the claim that a draft is involuntary servitude, and hence proscribed by the same Amendment that abolished slavery. The Court basically just laughed this claim out of court, basically just saying that something so noble as fighting to defend your country could never be the same thing as the degradation of slavery. But people didn't necessarily agree with the Court when conscription was new in the North. Of course you can't really make the argument anymore, because slavery has a kind of Godwin's Law-esque status that you're not allowed to compare anything to it. But on the merits, I think it's hard to argue that a draft isn't involuntary servitude, and we know that it's not clearly true that in the language of 1865 no one would've thought that the words "involuntary servitude" could refer to the draft. Maybe the draft is unconstitutional after all.