The notion of “involuntary servitude” was abrogated with the 13th Amendment. I don’t see how a military draft could ever be reconciled with that.
Bringing up the 13th Amendment brings up a novel point
“Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.”
The 13th Amendment does not prevent criminals from being sentenced to slave labor. Indeed, chain gangs were a common feature a century or so ago.